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I 


WASHINGTON  OBSERVATIONS  FOR  1875.— APPENDIX  II. 


RESEARCHES 


MOTION    OF    THE    MOON 


MAni;  Al    THE 


UxiTKi)  Statks  Naval  Oi5servat()RY,  WASHiNdiox. 


SIMON    NSAYCOMB, 

PROFESSOR,  V.  S,  NAVY. 


PART    I. 

REDUCTION  AND  DISCUSSION  OF  0BSF:RVATI0NS  OF  THK  MOON  BFFORE  1750. 


WASHINGTON: 

GOVERNMENT     PRINTING     OFFICE. 


1878. 


PREFACE. 


For  several  years  after  the  publication  of  Hansen's  Tables  of  the  Moon,  it  was 
very  generally  believed  that  the  theory  of  the  motion  of  tliat  bod}^,  after  liaving  been 
the  subject  of  astronomical  and  mathematical  research  for  two  thousand  years,  \>as 
at  last  complete,  and  that,  in  consequence,  the  motion  of  the  moon  could  now  be  pre- 
dicted with  the  same  accuracy  as  that  of  the  other  heavenly  bodies.  In  1870,  the 
writer  showed  that  this  belief  was  entirely  unfounded,  and  that  the  correctness  of  the 
tables  since  1 750  had  been  secured  only  by  sacrificing  the  agreement  with  observations 
previous  to  that  epoch,  so  that,  about  1 700,  Hansen's  Tables  deviated  more  widely 
from  observations  than  did  those  which  they  superseded.  It  was  also  shown  that  at 
the  time  of  writing,  the  moon  was  falling  behind  the  tabular  position  at  a  rate  wliich 
woidd  speedily  cause  a  very  serious  error  in  the  representation  of  the  Tables.  Alto- 
gether, it  appeared  that  notwithstanding  the  immense  improvement  whicli  Hansen  had 
made  in  the  accuracy  of  the  inequalities  of  short  period,  the  theory  of  those  of  long 
period  was  no  nearer  such  a  solution  as  would  agree  with  ol)servation  than  when  it 
was  left  by  Laplace. 

The  work  oT  reinvestigating  the  subject,  and,  if  possible^  of  ascertaining  the  cause 
of  these  deviations,  was  soon  after,  with  the  concurrence  of  Rear- Admiral  Sands,  made 
a  part  of  the  anther's  official  duty  at  the  Naval  Observatory.  It  may  be  proper  to 
i-emark  that  this  arrangement  was  largely  due  to  the  interest  taken  in  the  subject  by 
Captain  (now  Rear-Admiral)  Daniel  Ammen,  IT.  S.  Navy,  the  Chief  of  the  Bureau 
of  Navigation 

The  work  as  plaimed  was  divisible  into  two  distinct  parts:— 

1.  The  mathematical  theory  of  the  inequalities  of  long  period  in  the  moon's 
mean  motion.  As  the  only  cause  to  which  such  inequalities  could  be  attributed  was 
the  action  of  the  planets,  this  part  of  the  investigation  resolved  itself  into  a  compu- 
tation of  that  action. 

2.  The  study  of  the  inequalities  in  question  from  observations,  especially  from 
observations  before  1750.  In  the  ancient  and  modern  observations  of  eclipses  and 
occultations,  there  was  believed  to  be  an  immense  mass  of  valuable  material  for  the 
purpose  in  question,  some  of  which  had  been  almost  forgotten,  and  very  little  of  which 
had  been  discussed  with  modern  data. 

An  amount  sufficient  for  the  employment  of  two  computers  having  been  appro- 
priated by  Congress,  these  two  investigations  were  carried  on  siuuiltaneously,  with 
the  intention  of  completing  them  in  the  order  in  which  tiiey  have  been  named.  But 
as  the  mathematical  investigation  was  sujjposed  to  be  nearly  brought  to  a  close,  it  was 
found  that  certain  terms,  which  were  at  first  supposed  to  be  of  no  importance,  woidd 
have  to  be  investigated,  and  that  this  investigation  might  prove  the  most  tedious  part 
of  the  whole  work,  unless  some  method  of  shortening  it  could  be  devised.     Not  having 


PREFACF,. 


yet  been  able  to  decide  which  is  the  best  method  of  treatiiiff  the  sulyect,  the  invosti- 
jration  is  still  iiicoinpleto,  and  the  present  I'esearch,  orij^inally  intended  as  Part  IT,  is 
issued  as  Part  I. 

In  1 87 1,  advantage  was  taken  of  a  journey  in  Europe  to  ascertain  whether  the 
older  observatories  and  libraries  of  that  continent  might  not  contain  unpul)Hshed 
observations  of  eclipses  or  occultations  which  would  be  of  value  for  the  subject  in 
hand.  In  this,  an  unexpected  measure  of  success  was  attained.  At  I'aris,  M.  De- 
LAUNAY,  then  the  Director  of  the  Ob.servatory,  placed  all  the  archives  of  that  estab- 
lishment uiu'eservedly  at  my  disposal.  Among  this  material  were  most  of  the  original 
note-books  of  the  French  astronomers  from  1675  onward,  and  here  a  great  number  of 
occultations  were  found  to  have  been  observed,  though  the  observations  had  been 
totalh'  forgotten.  ^Phe  observations  published  in  the  Memoirs  of  the  Academy  were 
but  a  small  fraction  of  those  actually  observed,  and  that  fraction  was  compo.sed  of  the 
least  valuable  of  them. 

()ne  circutnstance  connected  with  these  observations,  while  greatly  increasing 'he 
labor  of  the  reduction,  has  also  increased  the  value  of  the  results  by  insuring  the 
entire  genuineness  of  tiie  records.  The  records  made  use  of  consisted,  in  large  part, 
of  the  original  rough  notes  of  the  observations,  without  any  explanation  whatever,  and 
without  any  reductions  excejjt  the  occasional  application  of  a  supj)osed  clock-correc- 
tion. In  perhaps  half  the  cases,  the  star  occulted  was  neither  named  nor  described, 
wliile  the  methods  of  determining  clock-error  had  to  be  ascei'tained  by  conij^arison 
and  induction.  Many  of  the  books  were  entirely  anonymous.  As  the  coj)ies  of  the 
records  of  which  use  has  been  made  are  given  in  full  in  the  present  paper,  a  minute 
description  is  not  here  necessary. 

At  the  observatory  of  Pulkowa,  1  was  fortunate  enough,  through  the  kind  offices 
of  Director  Struve,  to  find  what  might  be  con.sidered  as  the  complement  of  the  Paris 
observations  in  the  records  of  Dei.isi.k.'s  observations  at  St.  Petersburg  between  1727 
and  1747.  From  about  17^0,  there  was  a  great  falling-oft"  in  the  number  of  the  Paris 
observations,  so  that  those  of  .St.  Petersburg  come  in  very  o])portunely.  At  Pulkowa 
I  also  availed  myself  of  the  opjjortunity  of  making  use  of  the  umivalled  astronomical 
library  of  the  establishment  to  conn)lete  the  list  of  pul)lislied  data.  In  these  researches 
at  Pulkowa  I  was  actively  assisted  by  Dr.  Linde.njann,  then  acting  lil)rarian,  who 
devoted  several  days  to  this  work. 

Another  series  of  observations  which,  though  i)ublished,  seem  to  have  been 
nearly  forgotten,  was  found  in  the  Livre  de  la  Grande  Table  Jlakemitc,  translated  from 
an  Arabian  manuscript  by  Caussin.  These  comprise  the  most  valuable  of  the  Arabian 
observations,  but,  so  far  as  1  am  aware,  they  have  not  before  been  fully  compared 
with  modern  tables. 

The  want  of  accurate  data  in  the  beginning  has  'added  greatly  to  the  labor  of 
completing  the  present  work,  and  caused  nuich  imavoidable  delay.  In  the  case  of 
many  of  the  Paris  observations,  the  stars  coidd  not  be  identified  until  the  times  of 
observation  had  l)een  computed,  and  the  apparent  place  of  the  mOon  at  those  times  found 
from  the  tables.  Then  the  star  had  to  be  observed,  in  order  to  improve  the  means 
of  determining  its  proper  motion.    The  existing  data  for  deteraiining  the  places  of  stars 


PREFACE. 


two  centuries  back  wore  so  inHiiffi(;ient  that  a  I'oinplote  i-oiiivewtiyatidn  of  the  ri^lit 
asconHioiis  of  the  Htars  became  a  necessary  j)art  of  tlie  work.  '^I'liis  invostij^iition  was 
rendered  successful  by  Auwers's  re-reduction  of  Braoi.i'.y's  observations  ;  and  its  results 
have  in  part  been  published. 

It  will  be  seen  that  the  material  most  used  in  the  present  investigation  has  iiithcrlo 
been  least  known.  Possil)ly,  the  most  valuable  portion  of  it  is  found  in  the  un|)uli- 
lished  Paris  observations,  wlierel)y  tlie  moon's  mean  lon<>itude  is  determined  with 
astronomical  acciu'acy  from  1680  onward.  Tiie  observations  of  Gassendus,  Hevelius, 
and  Flamstked  (whereby  the  mean  lon<;itude  is  carried  back  with  gradually  dimin- 
ishinjf  accin-acy  a  half  century  farther),  thon<>ii  published,  have  never  been  used  for 
determining  the  moon's  place.  Nearly  .he  same  remark  will  apply  to  the  Arabian 
observations,  though  it  was  by  them  that  the  secular  acceleration  of  the  moon's  mean 
motion  was  first  determined.  On  the  other  hand,  the  ancient  total  eclipses  of  the  sun, 
which  have  been  so  nnich  discussed  during  the  present  century,  are  b(U"e  thrown  aside. 
The  reason  for  this  course  l)eing  given  in  the  ju'oper  place  need  not  be  rei)eated 
now ;  nor  will  the  writer  make  any  attempt  to  forestall  the  differences  of  ojnnion 
which  may  arise  respecting  its  validity.  He  will  only  remark  that  he  approached 
the  subject  without  any  bias  whatever,  unless  a  general  distrust  of  the  scientific  pre- 
cision of  ancient  authors  may  be  regarded  as  a  bias,  and  that  the  various  considera- 
tions which  presented  themselves  to  his  mind  on  examining  these  records  are  iiere 
reproduced  as  exactly  as  po.ssible.  While  the  result  of  the  examination  of  ancient 
solar  eclipses  has  seemed  to  him  to  jnstifj'  his  general  distrust,  that  of  the  lunar  eclipses 
in  the  Almaf/esf  lias  not.  Moreover,  no  part  of  the  discussion  has  l)een  altered  in  the 
light  of  the  result  finally  reached;  but,  verbal  revision  aside,  each  consideration  is 
given  as  it  was  originally  written.  The  only  a|)proach  to  an  excei)tion  occurs  in  §  2, 
from  which  he  has  expunged  a  derogatory  estimate  of  Ptolemy's  eclij>ses,  formed 
before  he  had  compared  them  with  the  fables.  The  lack  of  unity  and  consistency 
which  may  thus  have  arisen  in  a  discussion  which  has  been  growing  by  piecemeal  for 
six  years  may  be  excused  under  these  circumstances. 

The  date  i  750  is  fixed  ujion  as  the  terminal  point  of  the  investigation,  partly 
because  it  is  that  when  accurate  meridian  observations  commence,  and  also  because  it 
is  the  epoch  which  separates  the  period  within  which  we  have  readily  accessible  obser- 
vations and  copious  tables  of  reduction  founded  on  modern  data,  from  that  during 
which  both  these  recpxirements  are  wanting. 

In  conclusion,  the  author  wishes  to  place  on  record  his  appreciation  of  the  labors 
of  the  skilled  assistants,  without  whose  help  the  completion  of  the  work  would  not  have 
been  possible.  He  owes  much  to  the  conscientious  accuracy  of  his  young  friend,  Mr. 
Parker  Phillips,  who,  with  Mr.  Jonx  T.  Hedrick,  assisted  him  from  1871  until  1873. 
In  the  closing  parts  of  the  work,  most  of  the  necessary  computations  were  prepared 
by  Mr.  John  Meier  and  Mr.  W.  F.  McK.  Ritter.  His  engagements  rendering  it  diffi- 
cult to  read  the  proof-sheets  properly,  Mr.  D.  P.  Todd  has  taken  an  active  part  in  pass- 
ing the  work  through  the  press. 

Nautical  Almanac  Office, 

Washington,  April,  1878, 


ERRATA. 


Page    13,  line  5,  for  Bii.  60  read  Bd.  52. 

Page    42,  Eel.  No.  10,  for  s""  56'"  read  6''  56'". 

Page    44,  line  19,  for  +  18'  read  —  18'. 

Page    59,  line  21,  for  Lo  —  m"  read  Lo  +  111°. 

Page   60,  lines  4  and  5,  add  (7). 

Page    74,  lines  13  and  15,  for  ir  read  11. 

Page    84,  line  8  from  bottom,  for  cpi  read  99*. 

Page  205,  line  i,  add  §  t2. 

Page  231,  line  8  from  bottom,  for  3,8"  read  38". 


TABLE   OF  CONTENTS. 


§  I.— HISTORICAL  INTRODUCTION ,j 

Values  of  secular  acceleration  dediicfd  Ijy  DuNTHOKNE,  Tobias  Maykr,  Lai. ANDK,  iind  Lapiack      .     .     .  (j,  lo 

Researches  of  Zech,  Adams,  Hansen,  a'ul  Dei.aunay id 

Researches  of  Mavxk  and  r>f  Fi;Rnri.  on  tid.il   retaidalion ii 

AiRY's  discussion  of  ihc  ancient  solar  eclipses I2 

Hartwio's  comparison  of  Zkch's  discussion  with  Hansen's  Tables 13 

Inc(|ualitics  of  long  period  in  the  moon's  mean  motion 13 

S  2.— SUMMARY  OK  DATA  FOR  DKTERMIMNG  THE  APPARENT  SECULAR  ACCELERATION     .  17 

I.  Statements  of  ancient  historians  respecting  Qcrtain  total  eclipses  of  the  sun   .• 18 

H.  The  series  of  lunar  eclipses  recorded  by  Ptolemy  in  the  Almagfst irj 

HI.  The  Arabian  observations  liy  Ebn  JouNis 20 

IV.  Observations  by  Europeans  before  the  invention  of  the  telescope 21 

V.  Observations  made  with  the  telescope,  but  without  a  dock 22 

VI.  Observations  of  IIevei.ius 23 

VII.  Observations  approaching  the  modern  requirements  in  respect  to  precision 23 

VIH.  Observations  since  the  time  of  Bradley 2.) 

Conclusions  respecting  the  determination  of  the  secular  acceleration 25 

§  3.— DISCUSSION  OF  NARRATIVES  OF  ANCIENT  TOTAL  ECLIPSES  OF  THE  SUN      ....  27 

1.  The  eclipse  of  Thales 2S 

2.  The  eclipse  at  Larissa 30 

3.  The  eclipse  of  Xerxes 31 

4.  The  eclipse  at  Athens • 32 

5.  The  eclipse  of  Ennius 33 

6.  The  eclipse  of  Aoathoci.es 33 

7,8.  Other  ancient  and  mediajval  eclipses 34 

§4.— THE  PTOLEMAIC  ECLIPSES  OF  THE  MOON  RECORDED  IN  THE  ALMAGEST 35 

Accounts  by  Ptoi-emv.  accompanied  by  translations 35 

Tabular  data  for  eclipses  of  \he  Almagisl 41 

Equations  deduced  from  the  Ptolemaic  eclipses 43 

Resulting  corrections  to  Hansen's  tabular  mean  longitude 44 

§  5.— ARABIAN  OBSERVATIONS  OF  ECLIPSES,  FROM  CAUSSIN'S  TRANSLATION  OF  EBN  JOUNIS  44 

Observations  at  Bagdad  and  Cairo 45 

Tabular  positions  of  the  moon  and  the  sun  for  the  Arabian  observations 51 

Comparison  of  tabular  and  observed  times  for  the  Arabian  observations 52 

Results  of  the  comparison  with  Hansen's  Tables 54 

g  6.— MODE  OF  DEDUCING  THE  ERRORS  OF  THE  LUNAR  ELEMENTS   FROM  OBSERVATIONS 

OF  ECLIPSES  AND  OCCULTATIONS 55 

§7.— EFFECT  OF  CHANGES  IN  THE   LUNAR  ELEMENTS  UPON  THE   PATH  OF  THE  CENTRAL 

LINE  OF  AN  ECLIPSE 68 

§8.— OBSERVATIONS  OF  BULLIALDUS  AND  GASSENDUS 75 

Approximate  positions  of  stars  for  clock-error 76 

Observations  of  Bullialdus 77 

Eclipses  and  occultations  observed  by  Gassendus 79 

§  9.— OBSERVATIONS  OF  HEVELIUS] 88 

Position  of  Hevelius's  observatory 88 

Observations/romjhe  Machtna  Coelesiis 88 

Observations  from  the /4»nKr  C/tm«'/<n'(U.rJ in 


TABLE    OF    CONTENTS. 


-OUSICUVATIONS  IIV  ASTRONOMERS  OF  THE  FRENCH  SCHOOL  HETWEEN  1670  AND  1750 
rR:)M  MANIISCRIl'TS  AT  THE  I'ARIS  AMI  THE  IMM.KOWA  OHSERVATORIES 
Ri'iiiniks,  (Ifsiriinivc  :iiul  cxpLiiiitlnry,  on  ilif  iiispcciiiiii  iif  ilif  ni;iniisciipt 
Scries  I.— I'.x;unin;ilii)ii  uf  iii;iiuiscripls  ;it  llic  I'aris  Oljsi-rvatory      .      . 

OlisiTv.ilions  liv  C AhSiNl  anil  M arai.ui 

Sciies  II.— Ohsirvations  of  I,A  HiKi: 

Scries  III.— Oliservalinns  l>y  IJKl.lsl.i'  al  ni  iiiai  ilic  LiiMMiilinr^      .      . 
Series  IV.— Ohservatlons  by  llic  Cassinis  and  the  Makai  Ills      .      .      . 

Invesligalion  of  corrections  tii  the  I'aris  i|iiadraiit,  1706-1758 
Series  v.— Observations  In   1)11. isiK  at  St.  J'etersliiirg 


-I'OSITIONS  ol'    llli:    MOON   I'ROM    IIANSKNS  TAHLES.  USED  IN  COMPARING  THE  PRE. 

CEDINC  OUSERVATIONS  WITH  THEOUV 

(I)  Omission  ol  terms  unimportant  on  account  of  tlu^ir  minuteness 
(21  Modilii.alions  when  many  places  of  the  moon  are  to  lie  coniimted 

131  Terms  of  loiij^  period  produced  by  Venus 

Table  of  correctioiis  of  the  arguments  of  Hanskn's  Tables  for  terms  of  lo 

Tabular  positions  of  the  moon 

Observations  by  Fl.AMsri;i-,i) 

Clock-corrections — Fi.amstki.d 

Longitudes  and  latitudes  of  stars  for  tSfo 


"K  per: 


i.-DETAILS  OF  REDUCTION  OF  THE  OCCl'LTATIONS  .      .      . 

Tabular  exhibit  of  reduilion  of  the  occultations 

Occullations  obscived  bv  Hui.I.lALDUS 

Casskndus 

IIkvkmus  at  Uant/.iK 

the  Cassims  and  others  at  the  Paris  Observatory 

LaHirk 

Cassini,  Ki'c.^Scries  II 

Dki.isi.k  at  Luxembourg 

Dklisie  i.t  St.  Petersburg 

Fi  AMSTKia.  at  Greenwich 


od 


13.— EOUATIONS  OF  CONDITION  CiVEN  BY  THE  PRECEDING  OCCULTATIONS  OF  STARS 

l>rors  to  which  the  equations  are  liable 

Provisional  solution  of  the  iipiations 


14.— OBSERVATIONS  OF  KCLIPSKS  FROM   1620  TO  t 
Longitudes  of  the  sun  from  II ANSI  n's  Tables     .     .      . 

Details  of  reduction  of  the  eclipses 

Total  eclipse  of  1715,  May  2-3.  as  observed  in  England 


■24 


SI5' 


-DISCUSSION  OF  DEVIATIONS  IN  THE  MOON'S  MEAN  MOTION 
Individual  corrections  to  the  mean  longitude  of  the  moon      .... 

The  same,  graphically  interpolated 

Equations  of  condition  from  all  the  observations 

Changes  in  the  earth's  rotation  which  will  represent  deviations   . 

Representation  of  observations  by  a  periodic  term 

Table  of  corrections  to  Hansks's  mean  longitude  from  1620  to  1900 
(Comparison  of  this  table  with  observations 


;  lb.— MOTION  OF  THE  MOONS  NODE 

Path  of  moon's  shadow  over  England  during  the  total  eclipse  of  1715 
Correction  to  motion  of  moon's  node 


Vtge. 

116 
I  If) 
IlS 
130 
131 
148 
156 
156 
I7f. 


180 
i8g 
189 
I  go 
192 
196 
303 
303 

203 

205 
206 
206 
206 
207 
210 

2tl 
313 
316 
317 
221 

223 
223 
231 

236 
236 
237 
257 

261 
261 
263 
264 
265 
266 
268 
269 

270 
270 

274 


S  17.— CONCLUDING  REMARKS  ON  THE  VALUE  OF  THE  SECULAR  ACCELERATION  DEDUCED 

IN  THIS  PAPER 274 


RESEARCHES 


ON   THE 


MOTION   OF  THE  MOON. 


Paut  I. 

DISCUSSION  OF  OliSERVATIONS  MADE  PRKVIOIIS  TO  'IMFK 

YEAR  1750. 

IIISTOUICAL  INTRODUCTION. 

In  all  tlioorlcs  of  the  moon  before  the  beffiniiing  of  the  last  century,  tlio  moan 
motion  of  that  body  was  su])[)osc(l  to  be  uniform.  The  fir.st  inequality  discovered  was 
the  secular  acceleration.  While  the  general  proposition  that  a  comparison  of  ancient 
and  modern  eclipses  shows  the  mean  motion  of  the  moon  to  have  increased  since  the 
time  of  I'TOLKMy  is  no  doubt  duo  to  IIallky,  I  believe  the  first  careful  determination 
of  its  amount  is  that  by  Dijntiiokne.*  Going  backward,  in  the  order  of  time,  ho  com- 
pares his  tables  of  the  moonf  with  the  following  eclipses:  — 

Those  of  TycHo  Braiie  in  his  Progymnusmata ; 
Those  of  Waltheb  and  REaiOMONTANCS  (A.  D.  1478-90) ;  . 

Two  of  the  Cairo  eclipses  (A.  D.  977  and  978) ; 
Tlio  eclipse  of  Theon  (A.  D.  364) ; 
The  eclipses  of  Ptolemy. 
The  first  of  these  series  of  eclipses  was  too  near  his  epoch,  and  the  second  too 
unreliable,  to  predicate  anything  certain  upon.     From  an  examination  of  the  others, 
he  concludes  that  the  observed  times  will  be  best  satisfied  by  supposing  a  secular 
acceleration  of  10"  in  a  century. 

Soon  afterward.  Tonus  Mayer  deduced  an  acceleration  of  7"  from  the  eclipses 

of  the  Almagest,  which  value  ho  is  said  to  have  used  in  his  earlier  tables  of  the  moon. 

The  subject  is  next  discussed  by  Laland    in  the  Memoirs  of  the  French  Academy 

"  /'////.  Tmns.,  No.  492,  p.  162. 

t  These  tibles  were  probably  those  published  in  1759  ( f-ALANDR,  Biblhgmphie  A$tn»tom\que,  p.  410).  I  know  of  no  copy 
of  them  in  this  country, 

2 '75Ap.  2  0 


lO 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


of  Sciences  f'n"  the  yoiir  1 757.  Like  liar.LiVLDus  ami  others  of  his  conntiynion,  lie  has 
grave  douLts  of  the  honesty  Avith  which  i'i'OLEMY  lias  given  the  times  of  his  eclipses, 
ami  therefore  uses  only  the  fiist  of  the  series,  that  of  —  720.  He  adds  the  two  ecl'pses 
observed  at  Cairo  by  Ebn  JouNis,  A.  1).  977  and  978,  and  reported  in  the  introduction 
to  the  Historia  Coelestis  of  Tycho  Brake,  and  thence  concludes  that  the  secular  accel- 
eration is  about  9".886  per  century. 

Tlio  next  event  in  the  history  of  the  problem  is  the  discovery  by  Laplace  of  the 
physical  cause  of  the  acceleration,  and  his  calculation  of  its  amount,  which  he  fixed 
at  very  nearly  10".  The  exact  agreement  of  this  I'esult,  and  also  that  of  Plana,  with 
those  derived  by  Dunthorne  and  Lalande  from  observations,  seems  to  have  satisfied 
the  next  two  generations  of  astronomers  that  no  more  exhaustive  discussion  of  the 
ancient  eclipses  was  necessary.  We  find  an  acceleration  scarcely  differing  from  10" 
adopted  in  all  the  L;inar  Tables  between  those  of  Lalande  and  Hansen.  I  am  not 
aware  of  any  investigation  having  in  view  a  definitive  determination  of  the  secular 
acceleration  from  observations  alone  during  the  century  following  Lalande's  paper. 
We  have,  it  is  true,  two  important  papers  by  Zecii  in  a  series  of  memoirs  published  at 
Leipsic  under  the  general  title 

Preisschrijlcn  gelront  und  hcrausfjcffehcn  von  der  FiirstHch  JahJonowskischcn  Gc- 
sdlschaflzu  Leii)zig. 

The  two  papers  are:  — 

III.  J.  Zecii,  Aatrommischc  Untcrsuclnnigcn  iihcr  die  MomJ/imteinisse  des  Almagest. 
Leipzig,  185 1. 

IV.  J.  Zech,  Astronomisclic  UtitersHchmigen  iihcr  die  wicldigeren  Finstcrnisse,  tvelche 
von  den  Schrijistellcrn  des  classischcu  Altcrthmns  crirdhid  werdcn.     I^eipzig,  1853. 

The  first  of  these  papers  has  formed  the  basis  of  all  the  late  discussions  of 
Ptolemy's  eclipses;  but  the  author  finds  these  eclipses  inadequate  to  give  any  deter- 
mination of  the  moon's  secular  acceleration,  a  result  which  arises  from  his  including 
the  correction  of  the  moon's  mean  motion,  as  Avell  as  of  its  secular  acceleration,  in 
his  equations  of  condition.  If  we  determine  the  mean  motion,  not  from  the  modern 
observations  alone,  but  from  a  comiiarison  of  the  latter  with  those  of  Piolemy,  it  is 
evident  that  we  shall  have  no  accui'ate  data  rem.aining  with  which  to  determine  the 
secular  accelei'ation. 

In  1853  appeared  the  celebrated  paper  of  Adams,  whit'h  showed  that  the  theoret- 
ical value  of  the  secular  acceleration  found  by  his  predecessors  needed  a  large  diminu- 
tion. This  was  followed  by  several  accurate  calculations  of  its  amount  by  Adams 
himself  and  by  Delaunay,  the  latter  finally  fixing  it  at  6".  176.*  I  conceive  that  no 
rational  doubt  can  remain  that  this  result  represents  the  true  effect  of  the  gravitation 
of  the  planets  within  a  small  fraction  of  a  second. 

In  con.structing  his  Lunar  Tables,  Hansen  introduced  the  coefiicient  1 2".  1 8,  founded 
on  a  theoretical  computation.  A  revision  of  his  calculation,  leading  to  a  slightly 
greater  result,  namely,  I2".557,  is  given  in  his  Darlegung  der  theoretischen  Bcrechnung 
der  in  den  Mondtafeln  angewandten  Storiingcn  (ii,  p.  374).  About  the  time  of  publica- 
tion of  this  work,  Hansen  wrote  that  he  had  never  disputed  the  con-ectness  of  the 
result  of  Adams  and  Delaunay,  and  defended  his  result  rather  on  the  ground  of  its  • 

•  diHflts  Ktndiis,  1871,  i,  tome  72,  p.  495. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


II 


representing  uncieitl  observations  than  on  its  theoretical  correctness.*     It  can  therefore 
scai-cely  be  cited  as  tending  to  invalidate  the  resnlts  readied  by  these  investigators. 

It  has  long  been  recognized  that  there  was  no  necessity  for  an  agreement  between 
the  values  of  the  acceleration  derived  from  theory  and  from  observation,  becatise  a 
retardation  in  the  earth's  motion  of  rotation  would  produce  an  apparent  acceleration  in 
tlio  motion  of  the  moon,  and  the  friction  of  the  tides  must  produce  such  a  retardation. 
The  original  discovery  of  this  principle  is  attributed  to  Mayek;  but  it  would  seem  to 
have  been  lost  sight  offer  nearly  a  century,  when  it  was  taken  up  again  by  Fkrrel,  with- 
out any  knowledge  of  Mayer's  work.  Ferrel's  first  paper  was  i)ublished  in  1 853  in  vol. 
iii  of  Gould's  Astronomical  Journal.  It  contains  the  first  known  attempt  to  calculate  from 
theory  the  rettirdation  produced  by  the  action  of  the  moon  on  the  tidnl  wave.  Assum- 
ing that  the  tide  caused  by  the  moon  in  the  open  sea  is  two  feet  in  heigi  lul  that  it 
is  highest  two  hours  after  the  moon  passes  the  meridian,  he  finds  that,  if  the  ocean 
covered  the  earth,  the  equatorial  retardation  of  the  latter  would  amount  to  50  miles  in 
a  century.  Deducting  one  fourth  for  the  hand  surface,  he  finds  the  retarding  effect  of 
the  moon  alone  to  bo  37.44  miles  in  a  century,  and  the  combined  effects  of  the  sun  and 
moon  to  be  44.45  miles.  If  the  earth  were  really  retarded  by  this  amount,  an  apparent 
secular  acceleration  of  the  moon  amounting  to  84"  in  a  century  Avould  be  produced. 
As  no  such  acceleration  is  observed  e.\cept  what  is  otherwise  accounted  for,  he  con- 
cludes that  this  effect  of  the  sun  and  moon  must  bo  nearly  balanced  through  the 
gradual  contraction  of  the  earth  by  loss  of  temperature. 

After  the  researches  of  Adams  and  Delaunay,  and  the  general  concession  of  the 
correctness  of  their  results,  Ferrel  returned  to  the  subject  in  a  paper  on  The  Influence 
of  the.  Tides  in  causinfi  an  Apparent  Secular  Acceleration  of  the  Moon^s  Mean  Motion, 
read  before  the  American  Academy,  December  13,1 864.!  Reversing  the  process  of  his 
former  paper,  ho  finds  that  the  unaccounted-for  a2)parent  secular  acceleration  of  6"  cor- 
responds to  a  mean  retardation  of  the  tidal  wave  of  8  minutes,  or  to  a  retardation  of  10 
minutes  if  we  suppose  the  earth  to  be  cooling  according  to  FouRuui's  theory. 

Two  or  three  years  after  these  papers  by  Ferrel  were  published,  but  before  they 
became  known  in  Europe,  Delaunay  read  a  2)aper  before  the  French  Academy  of 
Sciences  on  the  same  subject, — Sur  Fexistence  cVune  cause  nouvelle  aijant  ime  influence 
sensible  sur  la  valcur  dc  Vcquation  seculaire  de  la  lune.X  Here  the  distinguished  author 
demonstrates  the  retarding  influence  produced  by  the  attraction  of  the  moon  on  the 
tidal  wave,  following  a  course  of  reasoning  similar  to  that  of  Mayer  and  of  Ferrel.  It 
was  through  this  paper  that  the  subject  was  first  brought  prominently  into  notice  arid 
discus&ion. 

Since  in  the  action  of  the  moon  and  the  cooling  of  the  earth  we  have  two  known 
causes  which  produce  a  secular  variation  in  the  mean  day,  the  accurate  effect  of  which 
cannoi;  be  computed  deductively,  it  will  probably  not  be  disputed  tliat  the  real  result 
to  be  derived  from  observation  is,  not  the  acceleration  of  the  moon's  mean  motion,  but 
tlie  retardation  of  the  earth's  rotation  on  its  axis.     Although  tlie  j)henomenal  effects 

*  Monthly  A'olices,  A'.  A.  S.,  vol.  xxvi,  p.  187.  Tliere  is  a  sliort  discussion  of  this  subject  by  Hansen  in  vol.  xv  of 
licrhhte  lii'r  Kimii^Uch  Siiilniuhut  Gi'sclisc/ia/l dir  IVis'  •schafloi  zii  Lcifzig,  Leipzig,  l86j,  in  which  he  discusses  tiilal  retarda- 
tion, and  defends  his  coelUcicnt  on  the  grounds  above  indicated, 

t  J'nvmiiiigs  of  tht  American  Academy  i>/  Arts  anil  Sciences,  vol.  vi,  p.  379. 

t  C'o/«//i'j' AV»(/«J,  tome  Ixi,  p,  I02J,  December  II,  1865. 


la 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


of  these  two  causes  are  nearly  identical,  they  are  not  absolutely  so.  The  longitudes 
of  the  sun  and  of  the  lunar  perigee  and  nodes  will,  in  fact,  be  affected  by  a  secular 
inequality  when  expressed  in  terms  of  a  variable  unit  of  time.  The  effects  of  these 
apparent  inequalities  are,  however,  too  minute  to  admit  of  detection  by  observation  for 
a  long  time  to  come. 

From  what  has  been  said,  it  will  bo  seen  that  the  value  of  the  secular  acceleration 
adopted  in  Hansen's  Lunar  Tables  can  hardly  be  considered  as  having  any  sufficient 
H  priori  foundation.  It  was  not  determined  from  observation  at  all,  but  from  theory; 
and  the  theory  was  so  incomplete  as  to  give  a  result  double  that  which  would  have 
been  given  by  a  complete  one.  If,  then,  the  result  agrees  with  observation,  it  can  only 
bo  because  tho  effect  of  the  omitted  terms  chances  to  bo  the  same  as  that  of  the 
earth's  tidal  retardation.  Whether  they  are  the  same  is  a  question  to  bo  settled  by 
observfitions,  especially  by  those  of  ancient  eclipses.  The  first  of  the  recent  discus- 
sions of  ancient  eclipses  having  this  object  in  view  was  made  by  Airy. 

In  the  riiilosopMcal  Transactions  for  the  year  1853,  he  has  a  paper  On  ihz  Eclipses 
of  Afjathocles,  Tliales,  and  Xerxes.  Tho  feature  of  this  paper  of  most  interest  at  tho 
present  time  is  the  historical  discussion  of  tho  circumstances  of  each  eclipse,  more 
especially  of  tho  localities  in  which  it  was  observed  to  be  total.  Tlie  computations  are 
made  from  I)e  Damoiseau's  Lunar  Tables,  with  the  iipplication  of  the  corrections  result- 
ing from  the  Greenwich  observations,  and  are,  for  the  purpose  in  question,  supereeded 
by  a  subsequent  paper.  Shortly  after  the  publication  of  Hansen's  Lunar  Tables,  Airy 
returned  to  tho  subject  in  a  paper  On  the  Eclipse  of  Atjafhocles,  the  Eclipse  at  Larissa, 
and  the  Eclipse  of  Thales.  With  an  Appcmlijc  on  the  Eclipse  at  Stiklastad,  in  the 
Memoirs  of  the  Itoi/al  Astronomical  Society,  vol.  xxvi.  Hero  he  niakes  use  of  the  places 
of  the  moon  calculated  by  Hansen  from  his  tables,  and  of  places  of  the  sun  from  Han- 
sen's Solar  Tables.  He  considers  the  following  conclusions  fairly  deduciblo  from  his 
investigation: — 

1.  Tlie  eclipse  at  Larissa,  — 556,  May  19,  is  established  as  a  real  eclipse  at  a  well- 
defined  point,  and  may  bo  adopted  for  critical  reference  in  deciding  on  the  value  of 
lunar  tables,  as  applicable  to  distant  places  of  the  moon. 

2.  Professor  Hansen's  Tables  very  well  represent  the  phenomena  of  the  three 
eclipses  of  Agatuocles,  Larissa,  and  Tiiales,  as  far  as  we  can  interpret  the  historical 
accounts  of  these  eclipses. 

3.  If  any  change  is  permitted  in  tho  two  elements  of  secular  ace  jloration  of  lon- 
gitude, and  change  of  tho  argument  of  latitude,  it  must  be  in  the  nature  of  increasing 
the  acceleration,  and  increasing  tho  argument  of  latitude  in  the  distant  ages. 

The  eclipse  at  Stiklastad  is  discussed  in  the  addendum  to  this  memoir.  Han- 
sen's Tables  throw  the  limit  of  totality  in  tho  case  of  this  eclipse  about  a  hundred 
mil'^s  south  of  Stiklastad.  To  make  the  eclipses  of  Stiklastad  and  Larissa  central,  it 
is  necessary  to  increase  Hansen's  secular  acceleration  by  o".8o9,  and  his  argument  of 
latitude  by  49"  X  uumber  of  centuries  preceding  1800.  Hansen's  sidereal  accelera- 
tion being  12".  18,  this  correction  increases  it  to  I2".99.  The  effect  of  these  coitoc- 
tions  is  said  to  be  to  throw  the  shadow-tracks  of  the  eclipses  of  Aoathocles  andof 
Tiiales  to  the  north,  and  nearer  the  points  over  which  the  historical  evidence  seems  to 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON, 


13 


indicate  tliat  they  passed.     In  the  opinion  of  tho  author,  a  strong  prosuniption  is  thus 
produced  in  favor  of  their  reality. 

A  comparison  of  Ptolemy's  series  of  hmar  ecHpses,  as  discussed  by  Zecii,  with 
Hansen's  Tables,  has  been  made  by  Hautwig,  and  published  in  tho  Astronom'ische 
Nachrichten,  Bd.  60.  A  clear  tabular  summary  of  his  results  is  i)rinted  in  tho  Month! if 
Notices  of  the  Royal  Astronomical  Society,  vol.  xxvi,  p.  185.  The  nineteen  eclipses 
indicate  a  sensible  negative  corx'ection  to  the  secular  acceleration,  the  mean  being 
—  I  ".9.  Only  three  out  of  the  nineteen  give  the  correction  positive ;  find,  if  we 
regard  the  series  as  consisting  of  observations  really  independent,  the  i)robablo  error 
of.  this  result  cannot  be  more  than  o".4,  and  its  reality  would  therefore  bo  beyond 
doubt.  The  result  of  these  eclipses  may  therefore  be  regarded,  from  this  point  of 
view,  as  incompatible  with  that  derived  by  Airy  from  eclipses  of  the  sun;  but  the 
stops  of  tho  investigation  are  not  given  with  sufficient  fullness  to  enable  us  to  judge 
of  the  reliableness  of  any  conclusions  which  might  be  drawn  from  it. 

It  will  be  seen  from  tho  foregoing  that  the  only  approach  to  a  definitive  answer 
to  the  question  the  question  what  value,  &c.,  what  value  of  tho  secular  acceleration 
is  deducible  from  observations,  is  to  be  found  in  the  papers  of  Professor  Airy.  If  we 
accept  the  three  most  ancient  eclipses  which  he  has  discussed  as  all  undoubtedly 
total,  then  scarcely  any  deviation  from  Hansen's  value  of  the  secular  acceleration 
seems  admissible.  But  I  cannot  conceive  that  the  historic  evidence  bearing  on  tho 
subject  places  the  phenomena  of  totality  so  far  beyond  doubt  that  a  discussion  of 
other  data  is  unnecessary. 

Such  a  discussion  is  the  more  necessary  because  it  has  been  known,  since  the  time 
of  liAPLACK,  that,  in  addition  to  the  uniform  acceleration  of  which  we  have  spoken,  the 
mean  motion  of  the  moon  is  apparently  affected  by  inequalities  of  long  period,  in  the 
satisfactory  explanation  of  which  geometers  and  astronomers  have  alw.ays  found  diffi- 
culty. The  first  discussion  of  such  .an  inequality  is,  I  believe,  that  of  Laplace,  in 
Mecanique  Celeste,  2*  partie,  livre  vii,  chap,  v,  under  the  title  Sur  une  inegdite  a  longue 
periode,  qui  paroit  exister  dans  le  motivcmcnt  de  la  lime.  Tho  discussion  is  mainly 
emi)irical,  the  existence  and  magnitude  of  the  inequality  being  inferred  from  observa- 
tions which  showed  that  the  mean  motion  of  the  moon  during  the  second  half  of  the 
eighteenth  century  was  greater  than  during  the  first  half.  It  was  then  assumed  that 
tho  inequality  Avas  a  periodic  one,  due  to  the  fact  that  twice  the  motion  of  tho  moon's 
node,  plus  that  of  its  perigfee,  is  a  very  small  quantity.  Tho  value  of  the  coefficient 
concluded  from  the  observations  was  47".5i,  and  the  expression  for  tho  resulting 

inequality  was 

47".5i  (=i5".39)  8in(2a5  +  ;r])-3TO).     . 

Using  Hansen's  notation  for  the  lunar  elements,  namely,  00  for  the  distance  of  the 
moon's  perigee  from  its  node,  and  oa'  for  the  distance  of  the  sun's  perigee  from  tho 
same  node,  tho  inequality  would  be 


I5".39  sin  (  <»-3  a>')  =  i5".39  sin  {173°  26'  +  (i'^  57'.4)  (t-  i8oo)l. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


The  following'  table  shows  how  the  observations  on  which  the  inequality  was 
predicated  were  found  by  Laplace  to  be  represented  by  it: — 


Date. 

Cor.  to  Lalande's 

Corrections  hy  the 

Error  out- 

Tables per  Obs. 

Formula. 

standing. 

i6gi  • 

-     13.58 

—     11.48 

+     2.10 

•  756 

0.00 

+       2.10 

+     2.10 

1766 

—       9.26 

.  -      9.54 

—     0.28 

1770 

-     28.09 

-     32.93 

-     4.84 

1789 

-     54*3* 

-     55.5a 

—     1.20 

1 801 

-     87.96 

-     85. 86 

+     2.10 

The  tables  compared  with  observation  were  those  in  the  third  edition  of  Lalanue's 
Tra'tte  iV Astionoiuk.  The  complete  formula  for  the  correction  of  their  mean  longi- 
tude, as  deduced  from  the  comparisons  in  the  second  of  the  above  columns,  was 

—  39".44  —  98".654  i  +  47".5 1  sin  (<»  —  3  t»') ; 

*  being  the  number  of  centuries  after  1750. 

It  would  seem  that  Laplace  was  by  no  means  satisfied  with  this  explanation  of 
the  cause  of  the  inequality,  as  he  afterward  favored  the  hypothesis  that  it  was  due  to 
an  unequal  compression  of  the  southern  and  northern  hemispheres  of  the  earth.  He 
found  from  theory  that  such  an  irregularity  in  the  confonnation  of  the  earth  would 
produce  an  inequality  in  the  moon^s  mean  motion  depending  on  the  same  argument* 
except  that  the  equinox  would'  have  to  be  substituted  for  the  sun's  perigee,  and  the 
function  cos  would  have  to  be  substituted  for  sin.  But  a  careful  analysis  afterward 
showed  him  that  this  cause  was  inadequate,  the  inequality  in  question  being  insen- 
sible on  any  reasonably  admissible  supposition  of  the  constitution  of  the  terrestrial 
spheroid.* 

The  question  was  next  taken  up,  from  a  theoretical  standpoint,  by  Poisson,  in  his 
Memoire  sur  le  mouvement  de  la  lune  autour  de  la  terre,  in  the  Memoires  de  V Academic 
des  Sciences,  tome  xiii,  pp.  209-325.  It  occurred  to  this  geometer  that  Airy's  inequal- 
ity of  long  period  in  the  motion  of  the  earth  due  to  the  action  of  Venus  must  involve 
a  corresponding  inequality  of  long  period  in  the  eccentricity  of  the  earth's  orbit,  and 
must  thus  produce  a  corresponding  inequality  in  the  secular  acceleration,  and  thence 
in  the  mean  longitude  of  the  moon  ;  but  the  computation  of  the  inequality  showed  it 
to  amount  to  only  two  hundredths  of  a  second.  In  his  account  of  this  memoir,  pub- 
lished in  the  Connaissance  des  Temps  for  1836,  p.  61,  Poisson  remarks,  "  II  est  facile  de 
s'assurer  que  Taction  directe  des  plan^tes  sur  la  lune,  ne  kaurait  non  plus  donner  lieu, 
dans  le  mouvement  du  satellite,  fi  aucune  indgalitt?  de  longjie  pdriode."  He  shows 
that  the  coefficient  of  Laplace's  first  inequality  is  absolutely  zero,  at  least  so  far  as 
the  terms  of  the  lowest  order  are  concerned.  The  hypothe  .is  of  an  inequality  in  the 
length  of  the  sidereal  day  he  also  considers  entirely  inadmissible.  He  hence  concludes 
that  no  inequality  of  long  period  should  be  admitted  in  tables  of  the  moon  founded  on 

*  CoHHaissamt  des  Ttmps,  1823,  p.  239. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


15 


theory.  As  to  the  existence  of  such  an  inequality,  lio  thinks  the  ohsorvations  are  too 
uncertain  to  ostablisli  it. 

It  was  reserved  for  Hansen  to  show  that  an  inequality  of  long  period  did  really 
result  from  the  theory  of  gravitation,  and  that  it  was  due  to  the  direct  action  of  a 
planet.*  He  first  computed  Laplace's  inequality,  and,  like  Poisson,  found  that  its 
coefficient  was  entirely  insensible ;  but  on  developing  certain  terms  in  the  action  of 
Venus  on  the  moon,  which  Laplace  and  Poisson  had  too  hastily  supposed  to  be  insen- 
sible, he  found  the  following  inequality  in  the  moon's  mean  longitude : — 

61  =  i6".o  sin  i-g  -  16  </  +  18  </"  -f  35°  20'); 

ff,  ff,  and  ff"  being  the  mean  anomalies  of  the  moon,  the  earth,  and  Venus  respectively. 
As  this  expression  still  failed  t"-  account  for  tlie  observed  inequalities  in  the  moon's 
mean  longitude,  he  carried  the  approximation  to  terms  of  the  fourth  order  with  respect 
to  the  disturbing  force,  and  found  that  the  terms  of  the  third  and  the  fourth  order 
increased  the  coefficient  to  2  7".4,  while  the  argument  remained  unaltered;"  so  that  the 
concluded  inequality  became 


27".4  sin  (-g-  16/ +  18^7"  +  35°  20'). 


,-4-ToJi(oiUoA  M  ^.Us*? 


But,  with  this  increase,  the  observations  were  hardly  so  well  represented  as  before. 
The  term  depending  on  the  argument  of  Airy's  equation  of  long  period  was  then  com- 
puted, and  the  coefficient  found  to  be  2  3".  2.     The  term  was 

61  =  23". 2  Hin  (Sg"- 13 g'  +  ^i 5°  30').  r/L' 

The  addition  of  this  term  to  the  other  he  considered  would  reconcile  theory  and  obser- 
vation. In  the  course  of  his  paper,  Hansen  remarks  that  he  did  not  employ  decimals 
enough  in  his  computation  to  be  able  to  pronounce  with  certainty  ayton  the  entire 
seconds  of  the  coefficients:  he  therefore  proposes  to  repeat  the  computation,  using  one 
or  two  more  decimals. 

The  periods  of  these  two  inequalities  are  respectively  273  and  239  years.  The 
difference  of  the  periods  is  so  small  that,  so  far  as  the  representation  of  existing  obser- 
vations is  concerned,  the  two  terms  might  have  been  combined  into  one. 

Hansen  concludes  his  paper  with  an  inquiry  whether  those  two  inequalities  will 
satisfy  the  observations.  He  has  before  him  the  corrections  to  De  Damoiseau's  theory 
given  by  the  Greenwich  observations  from  1 750  to  1 830,  and  he  finds  that  the  residuals 
will  be  satisfied  by  applying,  along  with  the  above  inequalities,  the  following  corrections 
to  the  moon's  mean  longitude  for  1 800,  and  to  its  mean  annual  motion : — 

Cori'ection  of  epoch  for  1 800 —  5".09 

Con-ection  of  mean  annual  motion -f  o".4096. 

He  also  makes  a  similar  examination  of  the  residuals  in  the  chapter  of  the  Me- 
canique  Celeste,  already  referred  to,  and  finds  that  these  may  be  represented  by  apply 
ing  to  Lalande's  positions  of  the  moon,  along  with  the  above  inequality,  the  following 
corrections : — 

Correction  to  mean  longitude  for  1 764 —  24".o 

CoiTection  to  mean  annual  motion —    o".23'jy. 

* Aitnmomhehi  NackrichUn  No.  597. 


IM^ 


i6 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Hansen  makes  no  inquiry  as  to  wliether  tlieso  two  sets  of  corrections  correspond 
to  the  tlifference  between  the  moon's  mean  longitiulo  and  mean  motion  given  in  the 
two  tables  compared,  and  so  lead  to  the  same  value  of  the  lunar  elements.  It  would 
not  bo  difficult  to  answer  this  question,  since  both  tnbles  are  extant,  but  the  answer 
would  bo  of  little  interest,  owing  to  our  ignorance  of  the  star  places,  equinox,  or  other  data 
on  which  Laplace's  observed  longitudes  rest.  The  writer  cannot  learn  that  any  details 
of  these  lal)oriou8  reductions  of  the  observations  of  FtiAMSTEED,  La  Hibe,  and  others 
were  ever  published,  and  his  efforts  to  find  the  original  manuscript  investigations,  which 
were  cordiallj^  seconded  by  the  late  lamented  Delaunay,  then  director  of  the  observa- 
tory of  Paris,  were  fruitless.  It  is  therefore  probable  that  the  whole  investigation  is 
lost  to  science. 
,    .  This  important  paper  is  dated  1847,  March  12.     The  next  announcement  from 

Hansen  is  seven  years  later,  and  appears,  as  a  letter  to  the  Astronomer  Royal,  in  the 
Monthly  Notices  of  the  Royal  Astronomical  Society  for  November,  1854  (vol.  xv,  p.  8). 
He  says: — 

"The  accurate  determination  of  these  two  inequalities  by  theory,  is  the  most  dif- 
ficult matter  which  presents  itself  in  the  theory  of  the  moon's  motion.  I  have  on  two 
occasions,  and  by  different  metl-ods,  sought  to  determine  their  values,  but  I  have  ob- 
tained i-esults  essentially  different  from  each  other.  I  am  now  again  engaged  with  their 
theoretical  determination  by  a  method  which  I  have  siniplified,  and  hope  to  bring  the 
operation  to  a  definitive  close." 

As  two  methods,  that  of  "successive  substitutions"  and  that  of  "undetermined  ' 
coefficients",  are  described  in  his  original  ))aper  of  1847,  and  the  results  of  each  given, 
it  seems  prol)able  that  these  are  the  two  methods  refeired  to.  If  so,  the  first  method 
gave  1 6".o  for  the  coefficient  of  the  first  inequality  and  zero  for  that  of  the  second, 
while  the  second  gave  27"  for  the  first  and  23"  for  the  second.  Wo  cannot 
decide  whether  the  proposed  computation  with  more  decimals  had  or  had  not  been 
executed. 

Our  next  information  is  obtained  from  the  completed  tables  of  the  moon  published 
in  1857.     Using  mean  anomalies,  the  expressions  for  these  terms  employed  in  the  tables 
are 
,,       .i-^U  1 5".34  sin (- ^ -  16 y-f  18/7" -1-33°  36') 

-f.2i".47sin(8/'-i3y  +  4°44'). 

The  first  of  these  terms  is  no  doubt  the  result  of  the  revised  calculation  described  as 

in  progress  in  the  letter  of  1854.     But  the  second  term  is  partially  or  wholly  empiri- 

-•^  \°[  ^iice^fA^  •'  X  ■     csvl,  it  being  found  necessary  to  alter  the  theoretical  value  to  represent  the  observations 

i-i.ioy  of  the  moon  from  1750  to  1850.     What  theoretical  value  Hansen  actually  found  by 

^  his  revised  computation  wo  do  not  know.     His  last  and  only  explication  of  the  matter 

is  given  in  a  letter  to  the  Astronomer  Royal  dated  1 86 1 ,  February  2,  a  translation  of 

which  is  found  in  the  Monthly  Notices  of  the  Royal  Astronomical  Society  {or  March,  1861 

(vol.  xxi,  p.  153).     He  says: — 

"For  the  rest,  I  have  found  the  coefficient  of  8V—  13E,  by  my  last  theoretical 
determination  of  it,  by  no  means  insensible,  like  Delaunay.  Without  the  introduction 
of  this  coefficient,  the  observations  show  deviations  at  different  epochs ;  but  with  the 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


17 


introduction  of  this,  these  deviations  disappeared  even  to  the  last  trace.  I  consider, 
therefore,  its  introduction  as  established,  and  reserve  to  myself  a  now  theoretical  deter- 
mination of  it,  b"t  cannot  take  this  in  hand  until  I  shall  have  proceeded  further  in 
the  calculation  of  the  remaining  coefficients.  I  have,  besides,  some  other  inequalities 
of  long  period,  which  are  caused  by  the  planets;  but  as  the  coefficients  of  these  ine- 
qualities are  small,  I  have  neglected  them  in  the  tables,  in  order  to  avoid  too  great 
extension." 

So  far  as  the  writer  is  aware,  this  is  the  last  utterance  of  Hansen  on  this  subject. 
In  his  Darlegting,  published  in  1865-66,  we  find  no  reference  whatever  to  these  terms- 

Delaunay  is  the  only  ot^'er  geometer  who  has  attacked  the  problem  of  these  ine- 
qualities. His  researches  arc  published  with  great  fullness  in  the  Additions  to  the 
Connaissance  des  Temps  for  1862  and  1863.  For  the  first  approximation  to  the  first 
inequality,  his  result  is 

i6".02  8in(-.9-i6/  +  i8/'  +  35°  2o'.2), 
a  result  almost  exactly  identical  with  that  first  given  by  Hansen  in  1847.     The  ulterior 
approximations  leiul  to  the  definitive  value 

i6".34  sin  (_^_,6y  +  i8<7"  +  35°  i6'.5), 
a  result  one  second  greater  than  the  definitive  value  adopted  by  Hansen  in  his  tables. 

In  the  case  of  the  second  inequality,  he  finds  a  coefficient  of  only  o".2  7,  a  quantity 
quite  insignificant  in  the  present  state  of  the  question.  We  here  find  an  irreconcilable 
difference  on  a  purely  theoretical  question,  on  which  no  light  has  been  thrown  within 
the  last  fifteen  years. 

That  the  subject  of  the  theoretical  computation  of  the  inequalities  in  the  moon's 
mean  motion  produced  by  the  action  of  the  planets  is  by  no  means  exhausted  appears 
from  the  recent  announcement  by  Mr.  Neison,  of  England,  that  he  has  found  an  ine- 
quality of  16  years,  due  to  the  action  of  Jupiter.  As  this  question  involves  that  of  the 
imiformity  of  the  earth's  rotation,  it  is  one  of  those  most  worthy  of  the  attention  of 


geometers. 


.  iy-A^- 


<5" 


§2. 


SUMMARY  OF  THE  IIATA  NOW  AT  OUR  DTSPOSAL  FOR  DETERMINING  THE 
APPARENT  SECULAR  ACCELERATION  OF  THE  MOON  FROM  OBSERVATION 
ALONE. 


It  has  long  been  tacitly  assumed  that  we  are  dependent  solely  on  the  accounts 
of  eclipses  transmitted  to  iis  by  history  for  the  data  necessary  to  prosecute  the 
investigation  in  question.  This  view  has  tmdoubtedly  been  correct  in  times  past. 
The  effect  of  the  cause  sought  increasing  as  the  square  of  the  time,  the  extreme  rough- 
ness of  the  ancient  observations  has  been  more  than  counterbalanced  by  their  remote- 
ness. For  instance,  if  the  mean  motion  of  the  moon  at  the  present  epoch  were  accu- 
rately known,  the  secular  accelei'ation  could  be  determined  equally  well  from  an 
observation  one  century  back,  and  from  an  observation  twenty  centuries  back  aff'ected 
with  an  error  four  hundred  times  as  great.  As  there  must  be  a  long  series  of  modern 
observations  to  determine  the  mean  motion  itself,  any  error  in  which  will  affect  the 
comparisons  by  which  the  secular  acceleration  is  to  be  determined  by  an  amount 
3 75  Ap.  2 


id- 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


increasing  ns  the  simple  time,  a  still  farther  advantage  is  thus  given  to  the  ancient 
observations.  We  may  see  this  advantage  in  the  strongest  possible  light  by  reflecting 
that,  with  a  vuluo  of  the  secular  acceleration  one  second  in  error,  the  motion  of  the 
moon  during  a  period  of  two  centuries  might  still  be  represented  without  an  error  of 
more  than  half  a  second. 

Notwithstanding  these  disadvantages,  I  think  the  time  has  an-ived  when  the  ob- 
servations mada  between  the  epocli  of  the  invention  of  the  telescope  and  the  year  1 750 
are  entitled  at  Ictast  to  consideration  as  a  means  of  determining  the  element  in  question. 
As  a  guide  toward  determining  what  observations  are  to  be  included  in  this  discussion, 
and  how  they  are  to  be  used,  it  is  proposed  to  give  a  brief  summary  of  all  the  data  at 
our  disposal  for  determining  positions  of  the  moon  before  the  year  1750,  and  to  esti- 
mate the  accuracy  with  which  the  secular  acceleration  can  be  found  from  each  class 
or  series  of  determinations,  supposing  the  necessary  favorable  conditions  to  be  fulfilled. 
Among  these  conditions  must  be  included  a  theory  of  the  inequalities  of  long  period 
which  shall  accurately  represent  observations  without  any  empirical  correction,  a 
desideratum  which,  as  we  have  shown,  astronomy  does  not  yet  possess.  The  observa- 
tions will  be  divided  into  classes  or  series,  each  class  or  series  presenting  some  common 
feature  by  which  the  data  are  to  be  judged.     Wo  begin  with 

I.  Statements  of  ancient  historians  from  ivhich  it  is  inferred  thnt  the  shadow  of  the  moon 
passed  over  certain  points  of  the  eartKs  surface  during  certain  total  eclipses  of  the  sun. 

If  there  were  even  a  feAV  cases  in  which  this  inference  could  be  drawn  without 
reasonable  doubt,  this  class  of  observations  would  doubtless  furnish  us  the  most  accu- 
rate data  we  possess  for  our  present  object.  Considering  only  the  eclipses  at  Larissa 
and  Stiklastad,  it  appears,  from  the  investigations  of  Airy  just  described,  that  the 
limits  of  the  value  of  the  secular  acceleration  within  which  both  eclipses  will  be  total 
are  very  narrow,  being  only  a  small  fraction  of  a  second.  But  it  seems  to  me  that 
there  is  in  nearly  all  these  descriptions  of  phenomena  too  much  vagueness  to  inspire 
us  with  entire  confidence  that  any  given  eclipse  was  really  total  at  the  supposed  point 
of  observation.  Reserving  for  the  special  discussion  of  each  eclipse  the  difficulties 
which  are  peculiar  to  it,  I  shall  here  mention  some  of  a  general  nature. 

The  first  difficulty  is  to  be  reasonably  sure  that  a  total  eclipse  was  really  tlie 
phenomenon  observed.  Many  of  the  statements  supposed  to  refer  to  total  eclipses  are 
so  vague  that  they  may  be  refeired  to  other  less  rai'e  phenomena.  It  must  never  be 
forgotten  that  we  are  dealing  with  an  age  when  accurate  observations  and  descriptions 
of  natural  phenomena  were  unknown,  and  when  mankind  was  subject  to  be  imposed 
upon  by  imaginary  wonders  and  prodigies.  The  circumstance  which  we  should  regard 
as  most  unequivocally  marking  a  total  eclipse  is  the  visibility  of  the  stars  during  the 
darkness.  But  even  this  can  scarcely  be  regarded  as  conclusive,  because  Venus  may 
be  seen  when  there  is  no  eclipse,  and  may  be  quite  conspicuous  in  an  annular  or  a 
considerable  partial  eclipse.  The  exaggeration  of  a  single  object  into  a  plural  is  in 
general  very  easy. 

Another  difficulty  is  to  be  sure  of  the  locality  where  the  eclipse  was  total.  It  is 
commonly  assumed  that  the  description  necessarily  refers  to  something  seen  where 
the  writer  flourished,  or  where  he  locates  his  story.     It  seems  to  me  that  this  cannot 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


J9 


bo  safoly  done  unless  tlic  statement  iu  mudo  in  connection  with  some  battle  or  n)ilitaiy 
movement,  in  which  case  we  may  presume  tlie  phenomena  to  have  been  seen  by  the 
army. 

II.  The  series  of  lunar  eclipses  recorded  hy  IHolemy  in  (he  Almagest,  and  used  by  him 
as  the  foundation  of  his  lunar  theory. 

These  are  nineteen  in  number.  Tliey  were  observed  at  Babylon,  Rhodes,  and 
Alexandria,  and  extend  over  a  period  of  eight  centuries.  Supposing  them  to  be 
affected  only  with  the  accidental  errors  of  observation,  the  comparisons  with  Hansen's 
Tables  made  by  IIaetwiq  seem  to  indicate  that  the  probable  error  of  each  recorded 
time  is  between  fifteen  and  twenty  minutes.  The  probable  error  of  a  mean  epoch 
derived  from  all  the  observations  will  then  be  about  four  minutes,  and  the  correspond- 
ing probalde  error  of  the  moon's  mean  longitude  will  be  2'.  iiiit  there  are  two 
circumstances  which  prevent  our  assigning  quite  this  degree  of  accuracy  to  Ptoifmy's 
record. 

The  first  is  applicable  to  all  observations  of  the  beginning  and  end  of  eclipses. 
It  is  that  the  first  contact  is  never  really  seen,  and  the  eclipse  can  never  become 
visible  until  a  sensildo  interval  qfler  the  time  of  real  contact.  We  must  expect  that, 
as  a  general  rule,  the  recorded  times  of  the  beginning  of  eclipses  will  be  too  late  by  a 
certain  sensible  amount,  and  those  of  the  end  too  small  by  an  amount  somewhat  less.* 
If  we  knew  that  the  observers  had  always  been  on  the  alert  for  the  eclipse,  and  keenly 
alive  to  the  necessity  of  seeing  it  at  the  earliest  moment,  and  of  noting  its  time  innne- 
diately,  some  estimate  of  the  intervals  in  question  might  be  made,  and  the  results 
corrected  accordingly.  But,  in  these  observations,  we  cannot  safely  apply  any  such 
estimate,  and  must  determine  the  sum  of  the  two  errors  from  the  discordances  between 
beginning  and  end.  In  the  case  of  eclipses  in  which  only  the  time  of  the  middle  is 
given,  we  have  no  means  of  knowing  whether  this  time  is  a  mean  of  observed  times 
of  beginning  and  ending,  or  whether,  in  the  case  of  partial  eclipses,  it  was  the  time 
when  the  observer  thought  the  eclipse  had  reached  its  greatest  phase.  Happily,  where 
beginnings  and  endings  are  both  observed,  the  errors  will  be  in  opposite  directions, 
and  will  partially  eliminate  each  other.  The  only  remaining  doubt  will  arise  from  our 
ignorance  of  the  amount  by  which  the  error  of  the  beginning  exceeds  that  of  the  end : 
in  general,  I  should  think  the  ratio  woidd  lie  between  1.5  and  2,  a  range  which  reduces 
the  outstanding  uncei'tainty  to  a  quite  small  amount. 

The  other  circumstance  is  that  the  observations  which  have  reached  us  are  not  a 
complete  series,  but  only  a  selection  made  for  the  foundation  of  a  theory— possibly  a 
preconceived  theory.  In  fact,  Ptolemy  has  been  strongly  suspected  of  selecting  such 
observations  from  the  records  as  would  make  the  results  fit  his  theory.  Bullialdus 
founds  this  accusation  upon  Ptolemy's  own  statement  that  Hippakchus  employed  a 
different  interval  between  two  of  his  eclipses  from  that  calculated  by  himself.  But  it 
does  not  seem  probable  that  one  who  had  dishonestly  altered  the  records  in  his  pos- 
session would  have  thus  frankly  stated  the  result  of  his  alteration.  It  seems  more  likely 
that  there  was  something  in  the  calculation  of  Hippakchus  which  Ptolemy  failed  to 
understand,  a  circumstance  not  at  all  improbable. 

*  Since  this  was  wrilten,  an  examination  of  eclipses  has  led  me  to  suspect  that  the  older  observers  often  anticipated  the  times 
of  their  actu.illy  seeing  an  eclipse  become  sensible  to  the  sight,  and  recorded  an  estimated  time  of  true  geometrical  contact. 


ao 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


My  own  juilgmont  of  tlio  roliabloiieHs  of  Ptoi-emy's  luiinr  eclipHCs  ih  foundod  on 
these  considorationH.  First,  tlioy  are  not  to  bo  acco})tod  without  quostion,  hocauso  the 
fact  tliat  Ptolemy  deduced  from  a  comparison  of  liis  own  ecjuiiutxes  with  those  found 
by  IIiPPARCHUs  the  same  erroneous  vahio  of  tlio  eciuinoctial  year  (365''  5''  55'"  12",  a 
quantity  too  great  by  6'"  26")  whitii  IIipparchi'h  himself  deduced,  leads  to  a  very 
strong  suspicion  that  his  observations  might  be  in  some  way  made  or  selected  to  fit  a 
preconceived  theory.  Yet  all  of  Ptolemy's  Almof/cut  seems  to  mo  to  breathe  an  air  of 
perfect  sincerity.  Wo  m\ist  remember  that  the  scientific  logic  to  which  a  selection  of 
observations  is  opposed  had  tlien  no  existence  in  men's  minds.  The  question  arises 
whether  we  have  any  strong  reason  to  fear  that  the  observations  quoted  by  Ptolemy 
were  selected  to  confirm  some  preconceived  theory  of  the  moon's  motion ;  and,  if  so, 
whether  such  a  selection  would  bo  likely  to  result  in  making  the  moon's  moan  longi- 
tude systematically  incorrect  during  the  eight  centuries  through  which  the  observa- 
tions extend.  Expressing  no  opinion  on  the  former  question,  I  am  inclined  to  answer 
the  latter  in  the  negative.  Even  if  there  was  such  a  selection,  it  was  probably  made 
in  favor  of  a  theory  of  the  moon's  mean  motion  founded  on  other  observations  now 
lost,  and  therefore  entitled  of  itself  to  weight.  The  elements  which  Ptolemy  sought 
to  determine  from  the  observations  in  question  were  so  numerous  that  it  does  not  seem 
likely  that  the  mean  longitude  of  the  moon  would  be  systematically  erroneous  through- 
out the  whole  series.  I  consider  that,  on  the  whole,  the  observations  in  question  are 
much  more  reliable  than  the  accounts  of  supposed  total  eclipses,  and  yet  that  their 
confirmation  by  independent  data  is  very  desirable. 

III.  Passing  over,  for  the  present,  a  number  of  isolated  observations,  all  deficient 
in  precision,  we  reach  the  observations  of  the  Arabian  astronomers.  We  have  already 
remarked  that  both  Dunthorne  and  Lalande,  in  determining  the  secular  acceleration, 
made  use  of  two  eclipses  observed  at  Cairo  in  the  tenth  century.  These  .seem  to  have 
been  derived  from  the  Prolegomena  to  the  posthumous  collection  of  Tycho  Brahe's 
observations,  published  under  the  title  of  Tlistoria  Codestis,  where  they  are  given  on 
the  authority  of  Schickard.  These  observations  were  derived  from  an  Arabic  manu- 
script belonging  to  the  University  of  Leyden,  of  which  lit<^lo  was  known  until  near 
the  end  of  the  last  century.  It  was  then  loaned  to  the  French  government,  and  a 
translation  was  made  by  Caussin,  and  published  by  the  government  in  1804,  under 
the  title  of  Le  Livre  dc  la  Grande  Table  Ilakemite.  The  greater  part  of  the  eclipse 
observations  had  previously  been  published  in  Memoires  dc  VInstitut  National  dcs 
Sciences  et  Arts. — Sciences  Mathcmatiques  ct  Physiques, — Tome  ii,  Paris,  An  vii ;  but  a 
few  changes  are  made  in  the  separate  edition. 

I  tlnnk  this  work  contains  what  are  entitled  to  bo  considered  the  earliest  astro- 
nomical observations  of  eclipses  which  have  reached  us.  Some  of  the  data  left  us  by 
Ptolemy,  Theon,  Albategnius,  and  others  may  be  results  of  astronomical  observations; 
but  in  no  case,  so  far  as  I  know,  have  the  quantities  actually  observed  been  handed 
down  to  us.  For  example,  we  can  neither  regard  midnight  nor  the  middle  of  an 
eclipse  as  capable  of  direct  observation;  but,  in  tb^  present  work,  wo  find  given  the 
altitudes  of  celestial  bodies  at  the  moments  of  beginning  and  ending  of  eclipses, — data 
which  are  not  likely  to  be  tampered  with  to  agree  with  the  results  of  calculation. 
The  entire  number  of  eclipses  recorded  is  twenty-eight,  of  which  both  beginning  and 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


91 


oiul  wero  usually  (>1)hoi'V(mI.  Tlio  iiltitutlos  aro  ^'ivou  somotinios  in  wluilo  (li>(,n-eo8  only, 
BOinetiiiieH  in  coarso  fractictus  <»f'  a  (U'<,'reo.  If  tlioy  wcro  always  f^ivt-n  to  tiio  really 
uoarcst  outiro  degree,  so  as  to  l)o  aH't'cteil  with  a  probaMo  (;rror  of  only  liftccn  min- 
utes, the  corrosponding  error  in  the  moon's  mean  longitude  would  average  aliout  forty 
or  fifty  8ec(uuls  of  arc,  arul  would  therefore  he  very  suuiU  in  the  mean  of  all  tho 
observations.  Tho  most  serious  .source  of  error  is  that  already  alluded  to, — tho  uncer- 
tainty how  long  after  tho  first  contact  the  eclipse  was  first  perceived  and  tho  altitude 
taken,  and  lutw  long  before  the  actual  end  it  was  lost  night  of.  It  is  not  of  much  uso 
to  guess  these  quantities  until  wo  discuss  tho  observations;  but  1  hope  that  tho  prob- 
abla  error  of  tho  mean  of  all  tho  observed  times  can  be  rediu-ed  to  1(^>^H  than  two 
minutes,  so  that  the  probable  error  of  the  moon's  mean  longitude  will  be  not  more 
than  a  minute  of  arc. 

IV.  Observations  hy  Enroiwans  before  the  invention  of  the  teleseope. 

liefjiomnntanus  and  Walther. — So  far  as  I  can  learn,  we  have  nothing  that  can 
l)roperly  bo  termed  astronomical  observations  of  eclipses  between  those  of  tho  Arabi- 
ans and  those  of  Keoiomontams  and  WAi/ruEu  in  tho  latter  i)art  of  tho  fifteenth 
century,  ily  authority  for  them  is  a  volume  containing  two  works,  piiged  sei)arately, 
under  the  respective  titles: — 

(i)  Cocli  et  Siderum  in  eo  crrantiitm  observntioncs  Jfassiacac  illustrisaimi  prinriina 
WUhehni  Ilassiae,  landf/ravii  aiispiciis  quondam  institidae  et  spicileyinm  biennale,  ... 
qitibiis  accesserunt  Joannis  Begiomontani  et  Bvrnardi  Waltheri  observationcs  Nuribergicae. 
Litgduni  Batavorum,  1 6 1 8. 

(2)  Johannes  de  Monte-Bcgio,  Gcorgii  PHerbarhii,  Bernardi  Widtheri  ac  alionini, 
eclipsium,  comctarmn,  planetarum  ac  fixarum  observationes.     .     .     . 

These  observations  belong  to  the  same  class  with  those  of  the  Arabians,  namely, 
altitudes  of  the  sun  or  moon  at  the  times  of  the  beginning  or  ending  of  tho  eclipses, 
and  do  not  seem  in  any  way  more  trustworthy.  The  telescope  not  being  known,  tho 
same  uncertainty  must  rest  over  the  question  of  the  exact  phase  at  which  the  eclipse 
became  visible  or  disappeared  from  view.  Tho  altitudes  are  given  only  in  coarse 
fractions  of  a  degree.  The  epoch  being  less  than  half  as  remote  as  that  of  the 
Arabian  observations,  the  coefficient  of  secular  acceleration  will  not  be  ono  fifth  as 
groat.     For  this  reason  I  do  not  consider  those  observations  worth  using  at  all. 

Tycho  Brahe. — The  observations  of  Tvcuo  follow  those  of  REdiOMONTANis  by 
about  a  century.  The  confused  manner  in  which  most  of  the  works  of  this  astron- 
omer have  been  edited  and  published  makes  exact  researches  into  their  subjects  rather 
difficult,  and  it  is  the  less  necessary  to  present  any  such  researches  that  I  have  de- 
cided to  make  no  use  of  the  observations.  I  have  been  led  to  this  course  by  the  fol- 
lowing considersitions.  The  telescope  was  unknown  to  Tycho.  Granting  that  the  most 
careful  observations  were  made  by  him,  the  probable  constant  error  of  contacts  observed 
without  a  telescope,  and,  without  any  means  of  determining  the  smallest  amount  of 
impingomont  of  the  moon  on  the  sun  or  of  the  earth's  shadow  on  the  moon  which  he 
could  see,  can  hardly  be  estimated  at  much  less  than  20".  A  number  of  accurately 
determined  times  of  contact  would  be  necessary  even  to  reduce  the  error  to  this 
amount.     After  devoting  considerable  time  and  labor  to  an  examination  of  what  i)ur- 


22  RliSKARCHES  ON  Tllli  MOTION  OK  THE  MOON. 

port  to  bo  tlio  obsorvationH  of  Tvciro,  both  tbo«e  printed,  aiul  thoso  in  nmnuHcript  at 
tlio  Paris  ( )bs»'rvatory,  I  waH  scarcely  ablo  to  find  what  (•(»uld  bo  ro>;ardod  an  nc(Uirato 
and  roliablc  oltscrvationH  of  edipHCH.  In  tbo  I'mfffniuasmatu,  tlioro  is  ..  hoHch  of  Honio 
Hiirty  «(dar  and  hmar  c«dipHo.s  obseived  by  liini  bctwoon  1572  and  .600.  Only  a 
sinjflo  tinio  iH  {fiven  for  eadi  otlipHO,  and  from  a  comparison  w;*!  tho  Uistoriu  Corkfitis 
it  may  1)o  conjt'citurcd  that  tlioso  aro  tho  timos  of  greatest  phaso.  Comparing  tlio  datoa 
in  tliis  Horit'rt  with  tho  ol)sorvntions,  winch  aro  arranged  in  chronological  order,  only 
some  of  tho  later  eclipses  were  to  be  fonnd  at  all.  Among  these  few  I  fonnd  scarcely 
an  muMinivocal  <d)servi)tion  of  tho  begimnng  of  an  eclipse,  and  only  occasional  obser- 
vations of  an  ending.  Tho  phases  were  given,  not  by  measnre,  bnt  by  drawing  u 
diagram  showing  how  tho  eclipse  appeared  from  time  to  time.  There  was  no  evidence 
that  these  diagrams  had  been  laid  down  by  measnre,  either  by  tho  astronomer  or  by  tho 
copyists  who  tbllowed  him.  It  was  generally  donbtful  whether  the  times  wore  api)a- 
rent  times,  or  those  of  one  or  the  other  of  two  clocks.  P^inally,  tho  discrepancies 
between  the  niannscript  and  the  observations  printed  in  tho  llistoria  Coclentis  were 
HO  nnmerons  as  to  destroy  all  confidence  in  either. 

It  is  wonderful  if  so  indefatigable  an  observer  never  observed  an  oc(udtati*»n  of 
a  star  or  planet  by  tho  moon,  yet  I  have  never  succeeded  in  finding  any  such.  I 
made  a  careful  examination  of  his  observations  during  tho  periods  in  which  occnltations 
of  Aldebaran  nuist  have  occurred  without  finding  any  allusion  to  such  a  phenomenon. 

V.  Ohscrvatinus  made  with  the  tclcscojic,  hid  without  a  clock. 

Ihdliithlits  and  lldsscHdiid. — The  ajjplication  of  tho  telescope  to  tho  observation  of 
eclipses  and  occnltations  m.ay  be  considered  as  connnencing  with  these  observers. 
They  had  no  clock,  "^llie  times  were  fixed  by  noting  the  altitude  of  the  sun  or  some 
bnght  star  at  the  moment  of  tho  jdienonienon.  GA.s.sKNDr.s  sometimes  had  an  assistant, 
who  used  the  quadrant,  while  ho  himself  noted  the  time  of  the  ))honomenon  by  a  signal. 

This  mode  of  observing  ought  to  be  susceptible  of  considerable  accuracy.  Gas- 
SENUUs's  (juadrant  seems  to  have  rend  at  least  to  5',  and  an  altitude  of  tho  star  to  tho 
nearest  5' would  generally  bo  equivalent  to  a  place  of  the  moon  to  tho  nearest  15". 
In  other  words,  the  probable  error  in  the  moon's  position  would  bo  only  about  4",  if 
the  altitude  were  really  noted  to  the  nearest  5'.  But  tho  observations  of  Gassenuus 
exhibit  anomalies  which  I  find  it  difficult  to  account  for.  Ho  frequently  gives  the 
altitudes  of  two  or  more  objects  corresponding  to  tho  same  occultation,  though  it  is 
quite  certain  that  only  ono  could  have  boon  observed  at  the  proper  moment.  In  these 
cases,  we  should  expect  the  second  altitude  to  give  a  time  systematically  a  little  later. 
Sometimes  wo  actually  find  it  so,  but  sometimes  it  is  earlier.  When  the  same  pair  of 
stars  are  thus  repeatedly  observed  in  the  course  of  a  series  of  occidtations  observed 
on  a  single  evening,  we  generally  find  tho  difl"erence  of  the  computed  times  nearly  the' 
same;  but,  another  pair  being  observed  at  another  time,  the  difference  changes  its 
character  entirely.  The  most  embarrassing'  case  is  that  of  the  occultation  of  y  Capri- 
corni,  1635,  August  26,  where  ho  gives  in  succession  tho  altitudes  of  a  Arietis,  tho 
moon's  limb,  and  a  Andromeda^  and  adopts  a  time  nonr  tho  mean  of  the  three  results, 
of  which  the  extremes  differ  more  than  three  minutes. 

I  have  found  no  other  case  so  bad  as  this.     The  general  agreement  of  the  obser- 


RKSEARCIIRS  ON  TIIF.  MOTION  OP  THE  MOON.  ,  i| 

viitioim  h  suc'li  tlmt  wo  niiiy  f;;om'riilly  conmilor  ouch  tiiiio  |fl.'»o  an'octed  with  ii  piolia- 
blo  error  not  (liH'crin;^  {^roatly  from  fifty  hoooikIh,  coiTcspoiidiiij,''  to  a  (•liaii;ro  of  25" 
in  tlw)  longitu(h)  of  tho  moon.  Wo  havo  no  means  whatever  of  jndg'in;,'  whether  tho 
olwervations  of  UiM.i.iALDua  aro  hotter  or  worse  than  those  of  CJa.s,s.,ni)i;s,  ami  so  may 
for  tlio  present  assimio  tliem  to  havo  tho  same  valne.  Wo  liavo,  in  tho  observations  of 
botli,  tlio  eijnivalont  of  al)out  twenty  observations  to  disposo  of;  and,  if  eacli  ^fivos  tlie 
moon's  lon<,ntndo  with  a  probaldo  error  of  15",  tlio  moan  of  all  may  bo  a.ssiimed  to  bo 
good  within  r»"  or  6".     Tho  moan  epoch  will  not  bo  far  from  1640. 

VI.  Ohscrcnlmis  of  JfcveUus. 

Tho  observations  of  IIkveliuh,  ns  given  in  his  Machina  ('odestis  and  Annua 
CUmactvrkus,  extend  from  1639  to  1683.  With  them  eommeneos  tho  use  of  tho  cloek 
in  the  observations  of  eclipses  and  occultations,  the  clock  being  regulated  I)y  observed 
altitudes  of  tho  sun  or  stars.  This  gives  us  more  definite  means  of  estimating  the  prob- 
ab.lc  errors  of  tho  observed  times,  which  may  bo  inferred  from  tiio  discordance  of  tho 
separate  determinations  of  clock-errvn-.  From  tho  best  estimate  wo  can  form,  tho  in-ob- 
able  error  of  tho  several  determinations  of  time  will  fall  between  20  laid  24  seconds. 
Taking  the  latter  limit,  tho  probable  error  .»f  each  determination  of  the  moon's  longi- 
tude will  bo  about  12".  Wo  havo  in  tho  Mork  of  Hevemcs  tho  apparent  equivalent 
of  about  f(»rty  average  occultations  to  dispose  of.  'J'he  probable  error  of  the  moon's 
longitude  which  results  from  tho  mean  of  all  his  observations  will  therefore,  if  no  other 
errors  than  such  accidental  ones  as  these  enter,  not  be  more  than  2".  Allowing  for 
probable  unknown  causes,  wo  may  estimate  it  at  3".     Tho  mean  epoch  is  about  1675. 

VII.  Observations  apiironchinr/  (he  nmJcrn  roiitireincnts  in  respect  to  precision. 
J'7amsteed. — Flamstecd's  observations  were  ma<le  on  the  same  .system  as  those 

of  Hevelius,  hut  with  far  greater  accuracy.  His  (puxdrant  was  sujjplied  with  "tcsles- 
copic  sights",  which  Hevelius  never  adopted,  and  by  which  tho  probable  error  of  the 
time  deduced  from  a  single  altitude  was  reduced  to  two  or  three  seconds.  Ilis  clocks 
wore  much  ])etter  than  those  of  IIevemu.s,  though  far  inferior  to  those  of  his  conten> 
poraries  on  tho  continent.  A  partial  drawback  to  these  advantages  is  that  his  clock- 
error  was  not  determined  often  enough,  nor  near  enough  to  tho  times  of  observations* 
Another  weak  ])oInt,  which  is  also  a  mark  of  IIeveliu.s'8  observations,  is  that  ho  never 
seems  to  havo  had  tlie  idea  of  eliminating  any  possible  index-error  of  his  quadrant  by 
altitudes  on  opposite  sides  of  the  meridian,  but  would,  month  after  month,  if  not  year 
after  year,  determii.j  nearly  all  his  clock-errors  by  observations  in  the  cast  alone,  or 
tho  west  alone.  An  estimate  of  tlieir  probable  error  would  therefore  bo  such  mere 
guesswork  that  I  shall  not  attempt  it. 

The  Paris  astronomers. — With  the  foundation  of  the  Pains  01)sorvatory,  a  yet  far- 
ther improvement  was  made  in  the  art  of  determining  the  time,  and  one  so  great  thijt 
the  observations  of  occultations  made  there  between  1680  and  1720  arc  frequently 
comparable  in  accuracy  wit'i  those  of  the  present  time.  The  mode  of  determining  tho 
clock-correction  was  substantiaii}  as  follows  : — A  quadrant,  gnomon,  or  meridian-mark 
was  set  as  nearly  as  practicable  in  the  plane  of  tho  meridian,  and  was  left  undistiu'bed 
in  position  during  long  intervals.     With  this  instrument,  the  clock-time  of  meridian 


24 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


transit  of  eai-li  limb  of  the  sun  was  assiduously  observed  on  every  day  that  the  weather 
permitted.  The  clock-time  of  meridian  passage  was  also  determined  from  time  to  time 
by  equal  altitudes  of  the  sun  on  the  two  sides  of  the  meridian,  observed  with  a  quad- 
rant. The  time  deduced  from  the  equal  altitudes  being  compared  with  that  deduced 
from  the  meridian  passage  gives  a  correction  to  the  meridian-instrument  applicable  to 
the  particular  altitude  of  the  sun  on  that  day.  The  correction  being  founcl  for  various 
altitudes  of  the  sun,  its  v.alue  for  any  particular  altitude  may  be  found  by  a  curve  or 
by  interpolation,  and  thus  the  correction  for  each  day  may  be  deduced. 

From  the  general  accord  ^nce  of  the  different  results  for  clock-error  and  for  the 
correction  of  the  meridian,  as  well  as  from  the  discordance  of  independent  observations 
of  the  same  occultation,  it  may  be  inferred  that  the  probable  error  of  a  time  well  deter- 
mined in  this  way  was  not  more  than  two  seconds,  corresponding  to  an  error  of  i"  in 
the  moon's  longitude.  This  is  so  small  that  it  does  not  exceed  the  probable  error  aris- 
ing from  the  irregularities  of  the  moon's  limb,  wliicli,  from  a  comparison  of  occulta- 
tions  observed  at  various  places,  would  seem  to  be  nearlj'-  i".  The  probable  error  of 
the  position  of  the  moon's  centre  will  therefore  vary  from  i"  to  i".4,  according  to  the 
point  of  the  limb  on  which  the  occultation  was  observed.  The  probable  error  of  the 
star  places  and  of  the  tabular  jjerturbations  is  larger  than  this,  and  may  bo  expected 
to  increase  the  probable  error  to  3".  After  gleaning  out  all  the  uncertain  observa- 
tions, we  shall  have  the  equivalent  of  more  than  sixty  good  occxdtations  observed 
at  the  Paris  Observatory  between  the  years  1680  and  1720.  These  ought  to  give 
the  mean  longitude  of  the  moon  for  the  epoch  i  700  wltliout  a  probable  error  of  more 
than  o".6. 

Of  the  same  class  of  observations  here  described  are  those  made  by  Delisle  at 
St.  Petersburg  between  the  years  1724  and  1748.  In  fact,  during  the  interval  1720 
to  1 753,  we  have  an  average  of  nearly  one  good  occultation  per  y  ar  at  St.  Petersburg 
and  Paris,  so  that  the  mean  longitude  of  the  moon  can  bs  fixed  during  this  interval 
within  one  or  two  seconds  of  arc. 


*  VIII.  Observations  since  the  time  of  Bradley. 
From  the  year  1750  to  the  present  time,  we  have  a  nearly  continuous  series  of 
occultatlons  and  eclipses,  observed  with  a  high  degree  of  accuracy  at  observatories 
whose  positions  are  well  known,  notably  those  of  Greenwich  and  Paris.  Of  course, 
these  observations  become  more  and  more  numerous  as  we  approach  the  present  time. 
Let  us  next  Inquire  how  accurately  the  mean  motion  of  the  moon  can  be  determined 
from  these  observations.  I  conceive  that  between  the  epochs  1780  and  1820  we  shall 
find  at  least  1 50  well-observed  occultatlons.  If  we  omit  a  third  of  these  as  being 
cases  where  the  star  was  too  far  from  the  line  of  motion  of  the  moon's  center  to  give  a 
good  determination  of  the  moon's  longitude,  we  shall  have  100  left  suitable  for  this 
determination.  If  we  take  the  probable  error  of  each  longlfudc  derived  from  a  single 
occultation  as  2".o,  which  I  think  is  not  far  from  the  truth,  the  piobable  error  of  the 
moan  of  all  will  be  o".20,  and  the  epoch  will  be  about  1800.  Allowing  for  systematic 
differences  between  observers,  it  may  be  increased  to  o".30.  Again,  from  the  more 
numerous  observations  on  l^oth  sides  of  the  epoch  1875,  wo  may  hope  to  obtain  the 
moon's  mean  longitude  for  that  epoch  with  the  same  precision.     By  a  comparison  of 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON: 


35 


the  two,  the  moon's  mean  motion  during'  the  first  seventy  years  of  the  present  centmy 
will  bo  obtained,  with  u  probable  error  of  o".4,  the  corresponding  epoch  being  1837. 
The  two  epochs  compared,  conjoined  with  the  observations  between  1820  and  1850,  will 
give  the  mean  longitude  for  '837  with  a  probable  error  which,  for  our  present  pur- 
poses, may  be  regarded  as  insignificant. 

Now,  suppose  that,  with  the  moan  longitude  and  mean  motion  thus  determined,  we 
carry  back  the  position  of  the  moon  to  the  epochs  of  the  observations  previous  to  1 720, 
and,  considering  the  difference  as  due  solely  to  the  secular  acceleration,  determine  the 
latter  from  the  comparison  of  the  observed  and  computed  longitudes,  what  will  be  the 
probable  errors  of  the  several  results  ?  The  probable  error  of  the  computed  mean  longi- 
tude will  be,  witli  sufficient  approximation,  o".6  T;  T  being  the  number  of  centuries 
from  1837.  If  we  represent  by  c  the  probable  error  of  the  mean  longitude  derived 
from  observation,  the  probable  error  of  the  comparison  will  be 

Vo".36r'  +  e', 
and  the  prol)able  error  of  the  value  of  the  secular  acceleration  deduced  from  the  com- 
parison will  be 

Vo^.36":PTe«  _ 

The  values  of  the  several  (|uantities  which  we  have  estimated  for  each  series 
of  observations  or  other  data  are  given  in  the  following  table,  the  last  sorie^  of  num- 
bers being  the  probable  error  of  the  secuLar  acceleration  which  would  result  from  a 
comparison  of  tlie  observations  with  a  lunar  theory  derived  from  observations  between 
1780  and  1875. 


D."ta  or  observers. 

T. 

1 

£. 

Ptolemy's  eclipses 

Arabi.in  eclipses 

Bi'Li-iAi-Dus  and  Gasskndus  .     .     . 

Hevei.ius 

Paris  and  Greenwich  astronomers  . 

21.4                200. 
8,3                   60. 

1.95       I              5- 
1.6                    3. 
1.35       i            0.6 

0.4 
0.8 

1.3 
1.0 
0.6 

From  this  reasoning,  we  may  draw  the  following  conclusion:— (?/•««</«//  the 
fundamental  premises  on  which  we  have  reasoned,  the  secular  acceleration  of  the  moon  can 
he  determined  with  nearly  the  same  order  of  accuracy  from  the  modern  as  from  the  ancient 
obser  nations. 

The  writer  is  quite  conscious  that  the  degree  of  accuracy  here  assigned  to  the 
results  is  something  to  bo  hoped  for  rather  than  expected,  and  that  many  astronomers 
may  consider,  not  without  some  reason,  that  the  degree  of  precision  attainable  has  been 
greatly  exaggerated.  To  judge  of  the  precise  state  of  the  question,  it  may  not  be  amiss 
to  present  some  considerations  on  the  premises,  expressed  or  implied,  from  wliich  we 
have  reasoned.     They  are  snb.stantially: — 

(i)  That  a  theory  can  be  constructed  which  sliall  accurately  represent  the  real 
and  apparent  inequalities  of  long  period  in  the  moon's  moan  longitude.  Tliis  involves 
4 75  Ar.  2 


26 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


the  three  conditions  that  the  motion  of  the  moon  is  aflFectod  only  by  the  gravitation  of 
the  known  bodies  of  the  solar  system ;  that  the  effect  of  this  gravitation  can  be  accu- 
rately calculated ;  and  that  the  motion  of  rotation  of  the  crust  of  the  earth  upon  its 
axis  is  invariable,  a  imiform  secular  retardation  excepted.  A  failure  in  any  one  of 
these  conditions  will  destroy  the  basis  of  the  preceding  calculation,  and  will  increase 
the  probable  eiTor  of  the  results  derivable  from  the  modern  observations  much  more 
than  in  the  case  of  the  ancient  ones.  It  is  useless  to  speculate  upon  the  probability 
that  these  conditions  will  be  fulfilled. 

(2)  The  other  hypothesis  is  that  the  observations  are  not  affected  by  any  system- 
atic error  nearly  as  great  as  the  probable  error  of  the  mean  derived  from  each  series  of 
ob.servations.  Among  the  sources  of  such  systematic  errors  are  to  be  included  errone- 
ous longitudes  of  observatories,  constant  instrumental  errors  in  the  determination  of 
time,  and  any  habit  peculiar  to  the  observer  by  which  he  systematically  observes  an 
occultation  differently  from  the  transit  of  the  sun's  limb  or  of  a  star. 

I  do  not  think  that  these  errors  will  very  largely  increase  the  probable  error  of  the 
results,  because  occultations,  if  actually  observed,  are  peculiarly  free  from  systematic 
error.  If  we  take  the  probable  errors  which  we  have  supposed  for  the  moon's  longi- 
tude at  the  three  epochs  1700,  1800,  and  1870,  and  reduce  them  to  time,  they  wil] 
amount  to  about  I'.a,  o".6,  and  o'.6  respectively,  (quantities  far  greater  than  the  average 
observed  personal  equations  between  different  observers.  Now,  we  have  tacitly  sup- 
posed it  an  even  chance  that  the  mean  of  u  series  of  observations  extending  over  a 
period  of  forty  years,  made  by  a  number  of  different  observers  and  in  a  number  of 
different  ways,  did  not  ^xc°ed.  i"  during  the  interval  1680-1720,  and  o".5  during  the 
interval  1780-1820,  and  I  do  not  think  this  estimate  will  seem  extravagant.  In 
regard  to  the  possible  erroneous  difference  of  longitude  between  Paris  and  Greenwich, 
it  is  to  be  remarked  that  observations  were  made  at  both  these  places  during  the  inter- 
vals we  have  been  considering,  and  in  such  numbers  that  the  error  will  be  nearly  elim- 
inated from  the  lunar  elements. 

However,  a  certain  and  perhaps  very  sensible  increase  in  the  probable  errors  of 
the  results  is  no  doubt  to  be  looked  for;  bijt  a  partial  or  entire  set-off  against  them  is 
to  be  found  in  the  fact  that  more  obse  •ations  are  actually  av.iilable  than  we  have  sup- 
posed to  be  included  in  forming  the  L  isis  of  our  theory,  and,  when  these  are  added, 
the  precision  of  the  result  will  be  sensibly  increased. 

In  the  preceding  enumeration,  I  have  included  only  classes  or  series  of  'observa- 
tions. In  addition  to  these,  there  is  a  great  number  of  isolated  observations,  both  ancient 
and  modem,  of  every  variety  of  excellence,  which  I  have  not  deemed  it  necessary  to 
enumerate,  because  their  value  can  be  determined  only  by  comparison  and  discussion. 
They  will,  of  course,  add  slightly  to  the  accuracy  of  the  data  for  the  final  determination 
of  the  required  element.  Altogether,  I  think  there  would  be  room  to  hope  that  we 
might  obtain  the  secular  acceleration  from  the  modern  observations  alone,  with  a  prob- 
able error  of  scarcely  more  than  half  a  second,  if  only  the  long-period  inequalities  in 
tiie  moon's  motion  were  conclusively  set'^ed.  This  is  something  which  is  still  in  the 
future.  .  ■ 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


27 


§3.  -■  ■■-.;         •        : 

DISCUSSION  OF  THE   NAUltATIVBS  OF   ANCIENT   UISTOKIAN3  FUOM  WHICH  IT 
.    HAS  BEEN  INFERRED  THAT  THE   SHADOW   OF   THE   MOON   PASSED   OVER 
CERTAIN    POINTS    OF    THE    EARTH'S    SURFACE    DURING    CERTAIN    TOTAL 
ECLIPSES  OF  THE  SUN. 


The  general  difficulties  in  tlie  way  of  obtaining  any  approach  to  certainty  re- 
specting the  totality  of  these  eclipses  have  been  discussed  in  the  preceding  section. 
We  now  pass  to  the  special  circumstances  of  each  eclipse.  The  following  is,  so  far  as 
I  am  aware,  a  complete  list  of  the  eclipses  in  question  which  the  accounts  of  the 
narrators  have  been  supposed  to  justify  us  in  considering  total.  They  are  arranged 
in  chronological  order,  and  are  selected  without  respect  to  their  confirmation  by  the 
tables. 

1.  The  eclipse  of  Thales,  —584,  May  28,  of  which  the  original  narrative  is  in 
Herodotus,  i,  74.  The  eclipse  is  also  mentioned  by  Plinv,  Hist.  Nat.,  ii,  1 2,  and  by 
Cicero,  De  Bmnatione,  i,  49.  This  eclipse  has,  perhaps,  been  the  subject  of  more 
discussion  during  the  present  century  than  any  other  of  tiiose  under  consideration. 

2.  The  eclipse  of  Larissa,  —5  ,6,  May  19,  discussed  by  Ahjy  in  the  Memoirs  of 
tlie  Royal  Astronomical  Society,  vol.  xxvi,  and  by  Hansen  in  his  Barlegung,  11,  p.  376. 
The  original  narrative  is  found  in  the  Anabasis  of  Xenophon,  ill,  4. 

3.  Tlie  eclipse  of  Xerxes,  about  —479,  described  by  Herodotus,  Hist.,  vii,  37. 
This  eclipse  has  never  been  identified  astronomically.  Reference  may  be  made  to 
AiRv's  paper  in  the  Philosophical  Transactions,  and  to  Zech's  prize  memoir,  already 
quoted. 

4.  An  eclipse  at  Athens,  —430,  August  3,  mentioned  by  Thucydides,  Hit^t.,  11,  28. 
This  eclipse  is  No.  2  of  Zech's  list. 

5.  The  eclipse  of  Ennius,  —399,  June  21,  quoted  from  Ennius  by  Ciceko,  De 
Itepublica,  i,  16,  discussed  by  Hansen,  Darlegintg,  ii,  p.  386. 

6.  The  eclipse  of  Agathocles,  —309,  August  14,  described  by  Diodorus,  Bihl. 
Hist.,  XX,  5,  and  by  Justinus,  Hist.  Vhilip.,  xxii,  6.  This  is  No.  9  of  Zech's  list,  and 
is  very  fully  discussed  by  Airy  in  the  Philosophical  Transactions  for  1853,  and  in  his 
second  paper  {Mem.  II.  A.  S.,  xxvi),  as  also  liy  Hansen  in  his  Darlcgnng,  ii,  p.  382. 

7.  Eclipse  of  334,  July  17,  No.  15  of  Zech's  list,  which  might  have  been  total  in 
Sicily  from  the  description  of  Fermicus,  Mat.  Ast.,  i,  2. 

8.  Eclipse  of  364,  June  16,  described  by  Ammianus  Marcelmnus,  Per.  Gest.,  xx, 
3,  as  total  at  Eoos. 

The  author  not  being  himself  versed  in  the  Greek  languiige,  the  original  nar- 
ratives of  these  several  eclipses  were  submitted  to  Professor  Huntington  of  the 
Columbian  University,  who  kindly  furnished  translations  and  critical  renderings  of 
the  several  passages  which  have  been  used  in  the  discussion.  In  general,  it  has  not 
been  deemed  necessary  to  quote  the  original;  but  wherever  this  seemed  requisite  to 
form  a  judgment  of  the  subject-matter,  it  has  been  done. 


28 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


"Now  after  this  (for  Alyattbs  did  not  by 
any  means  surrender  tlie  Scytliians  at  tbe  demand 
of  CYAXAREs)tlierewaswar between  tbe  Lydians 
and  tbe  Medes  for  the  space  of  live  years,  in 
which  [periodj  the  Medes  often  con(|uercd  the 
Lydians,  and  tbe  Lydians,  in  turi>,  the  Medes. 
And,  in  this  time,  tliey  also  bad  a  night  engage- 
ment; for  as  they  were  protracting  the  war  with 
equal  success  on  each  side,  in  a  battle  that  oc- 
curred in  the  sixth  year,  it  happened,  as  tbe 
armies  engaged,  that  tbe  day  wa^  suddenly 
turned  into  night.  Now  tiiis  change  of  day 
[into  night]  Tualks,  tbe  Milesian,  bad  predicted 
to  the  louians,  placing  as  tbe  limit  of  the  period 
[within  which  it  would  take  place]  this  very 
year  in  which  it  did  actually  occur.  Now,  both 
tbe  Lydians  and  the  Medes,  when  they  saw  night 
coming  on,  instead  of  day,  ceased  from  battle, 
and  both  parties  were  more  eager  to  make  peace 
with  each  other." 


1.— THE  ECLIPSE  OF  THALE8. 

(-584,M.iy28.) 

The  account  by  Hekodotits  is  as  follows.  Professor  Huntinoton's  translation  is 
annexed: — 

Hd.,  i(KA.),  74. 
J/iT«  Ss  TUUTa  {lit)  yap  Sij  i  'i^Aodrrijf  iisSiSiiu  Ttih^ 
^xiiOa^  i;aiTiiii>Ti  Kua^d/Jti)  i:iiXsixoj  Toiat  Auihitirt  xai 
TiiiiTi  .Vijdi)iiri  iysyi'ivss  ii:  e'rsa  TthTV  iv  TnXm  noXXiUt^ 
iiiv  III  M/jHiii  Tiiui  AuSiih;  IvixT/aav,  itnkhUi-.  lik  iil  Auii,i\ 
Tiih;  )fij3iiui'  Iv  St,  xtt\  vyzn(//a;fi'ijv  Tmii  iKiiirjaanTii, 
SiaifipuoiTi  Si  iripi  'si  j'lrijT  tov  KiiXs'iiiv,  tui  Sxtio  srsi 
(Tuii^idrji  j-si'd/i^vjjj,  iTU'^rjvstxs  were  r^?  /J"'/'iT  Toyiirrs- 
lomjt  TifV  iiiiiprfV  i^anhrji  -^uxTa  ysviaOat,  Tijv  Se  /j.;ro.X- 
X.ayr/V  Ta'JDjy  T^f  rjni/ir/^  Sa/.f/i  6  .ViAij'tfii)?  riiTiTi  "luxii 
~piirjdf)iuac  liteaOai,  imnvv  TrpiiOiiisyii^  IvtauTuv  tuDtwi/, 
iv  u>  St/  xal  iyl/sro  ij  iisTa,3iiXij.  iil  Ss  AuSni  re  xat  iil 
J//J<5f)!  imi  re  stSov  vuxra  dvTi  ^/lipr/i  ytvii/iinrji/,  rfj^ 
l^''X1^  T£  ItsauaavTii,  xa\  ixakXi'iv  rt  earrsuirav  xat  riiKipi'iTS- 
put  elpijvr^v  iwuTinirt  yivlirOat, 

Among  the  ancient  solar  eclipses,  this  is  the  one  which  has  been  the  most  cele- 
brated, and  has  given  rise  to  most  discussion  in  recent  times.  Yet  the  proof  of  its 
reality  seems  to  me  by  no  means  convincing.  It  is  true  that  we  may  consider  the 
three  following  propositions  to  be  individually  sufficiently  well  estabH.shed:  — 

(1)  That  a  battle  between  the  Lydians  and  the  Medes  was  ended  by  an  apparently 
sudden  advent  of  darkness,  substantially  as  described  by  Hekodoti:h; 

(2)  That  on  May  28,  584  B.  C,  the  shadow  of  the  moon  pa.ssed  over  Asia  MinoF, 
as  computed  from  the  tables; 

(3)  That  Thales  predicted  eclipses. 

But  that  these  propositions  all  refer  to  one  and  the  same  event  I  see  no  sufficient 
reason  for  holding.  Their  connection  may  well  be  real ;  but  its  reality  is  not  so  well 
established  that  I  should  be  willing  to  predicate  anything  respecting  the  changes  of 
the  lunar  elements  upon  it.  It  seems  to  me  that  commentators  on  this  eclipse  have 
not  sufficiently  distinguished  between  the  jjlienomenon  as  seen  by  the  contending 
armies,  and  the  conclusions  drawn  by  the  lonians  that  that  phenomenon  "as  what 
their  favorite  philosopher  had  predicted. 

The  simple  event,  as  described  by  Heuouotus,  and  as  wo  may  suppose  it  to  have 
been  described  by  the  eye-witnesses,  would  hardly  even  suggest  an  eclipse  of  the  sun, 
or  anything  else  more  extraordinary  than  the  regular  advent  of  night,  except  for  the 
single  word  i^aTn'ytj?  (suddenly).  But,  in  the  ardor  of  battle,  the  combatants  are 
apt  to  be  nearly  oblivious  of  the  lapse  of  time,  and  the  gradually  increasing  darkness 
of  evening  might  well  bo  unnoticed  for  some  time,  so  that,  when  it  at  last  interfered 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


n 


wltli  tho  progress  of  the  battle,  it  would  seem  to  have  come  on  moro  rapidly  thsin 
usual.  Tiie  formation  of  a  very  dark  heavy  cloud  about  sunset,  or  shortly  after,  such 
a  one  as  is  seen  fifty  times  to  one  occurrence  of  a  total  eclipse  of  the  sun  in  any 
given  place,  might  render  the  description  literally  true.  If  it  be  urged  that  the  making 
of  peace  indicated  something  extraordinary  or  impressive,  wo  may  rejoin  that  there  is 
nothing  in  the  account  to  indicate  it;  that  if  the  phenomenon  was  really  that  of  a 
total  eclipse,  the  night  must  have  turned  back  to  day  again  almost  before  the  fight- 
ing could  stop,  a  fact  which  the  historian  does  not  mention;  and,  finally,  that  the 
term  vvHTOfiaxt'tfy  would  hardly  apply  to  the  case  of  a  battle  stopped  by  a  total 
eclipsa  in  which  tho  darkuess  lasted  only  a  few  minutes  and  tho  battle  ('eased  as 
soon  as  darkness  commenced. 

This  view  of  the  naked  narrative  will  not,  I  conceive,  be  disputed.  TJie  evidence 
in  favor  of  an  eclipse  rests  entirely  on  the  construction  put  upon  the  account  by  the 
lonians,  or  some  other  parties  to  whose  ears  the  narrative  came.  It  cannot  be  sup- 
posed that  the  combatants  knew  anything  about  Tuales  or  his  eclipse,  so  they  cannot 
be  the  authority  for  supposing  that  the  darkness  was  that  predicted  by  Thales.  Our 
belief  in  the  eclipse  therefore  rests  on  our  faith  that  the  lonians  heard  a  different  story 
of  the  battle  from  that  given  by  Herodotus,  and  that  they  put  a  correct  interpretation 
on  the  circumstances.  In  trying  to  form  a  judgment  whether  they  did  so,  we  must 
take  into  account  what  we  know  must  have  been  the  nature  of  the  prediction,  as  well 
as  the  narrative  of  the  phenomenon;  because  it  is  on  the  agreement  of  the  two  that 
all  the  evidence  in  favor  of  the  re.ality  of  the  eclipse  rests.  Now,  keeping  within  the 
limits  of  historic  probability,  TuAf.ES  could  not  have  had  any  other  data  for  prediction 
than  a  knowledge  of  the  Saros,  which  gave  the  order  in  wliicli  eclipses  would  occur, 
and,  at  the  most,  such  knowledge  of  the  motions  of  the  sun  and  moon  as  would  enable 
him  to  judge  whether  a  given  conjunction  was  nearly  central,  and  at  what  time  of  day 
it  would  occur.  lie  could  not  possibly  have  predicted  that  tho  eclipse  would  bo  total 
and  that  day  would  be  turned  into  night,  and  could  scarcely  have  decided  whether  it 
would  or  would  not  have  been  visible  in  Ionia  even  as  a  partial  one.  If  he  coidd 
predict  one,  he  could  predict  two  or  three  every  year,  witliout  being  able  to  say  with 
any  certainty  in  what  places  any  of  them  would  be  visible.  But  any  such  prediction 
necessarily  involves  a  knowledge  of  the  exact  day  of  occurrence  of  the  eclipse,  and 
thus  the  only  means  by  which  the  lonians  could  identify  the  phenomenon  would  be 
the  coincidence  of  the  day  of  its  occurrence  with  that  of  the  prediction.  Now,  it  is 
remarkable  that  the  narrative  says  emphatically  that  the  year  was  correctly  predicted, 
but  makes  no  reference  to  the  yet  more  striking  prediction  of  tlie  day. 

Astronomically,  we  are  not  directly  concerned  with  the  jirediction  of  Thales,  but 
only  with  the  question  whether  the  circumstance  described  by  Herodotus  was  really 
the  total  eclipse  which  we  know  octurred  in  Asia  Minor  or  its  neighborhood,  H.  C.  584. 
The  prediction  is  important  only  for  the  reason  that  its  mention  by  the  historian  fur- 
nishes the  only  evidence  in  favor  of  the  phenomenon  being  really  an  eclipse.  Another 
very  weak  point  in  the  evidence  is  that  we  have  no  historic  data  for  deciding  who 
first  drew  the  conclusion  that  the  darkness  which  stopped  the  battle  was  that  of  the 
predicted  eclipse.     It  may  have  been  the  lonians,  it  may  have  been  some  writer  to 


30 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


whose  knowledge  the  occurrences  came,  and  it  is  quite  consistent  with  the  character 
of  Hkrodotus  to  suppose  that  it  may  have  been  liimself.  Since,  as  we  liave  seen,  th.; 
identification  could  only  have  properly  rested  on  the  coincidence  of  the  day  of  the 
prediction  with  that  of  the  battle,  and  since  the  historian  mentions  only  a  coincidence 
of  year,  if  we  accept  the  eclipse  we  must  suppose  that  the  most  striking  and  important 
circumstance  was  dropped  from  the  narrative  during  the  interval  between  the  identi- 
fif.ation  and  the  narration  by  the  historian.  If  the  historian  himself  drew  the  conclu- 
sion, without  any  other  data  than  those  he  gives  and  those  with  which  we  may  suppose 
him  to  have  been  acquainted,  then  the  entire  evidence  falls  to  the  ground. 

Let  us  now  consider  what  we  may  suppose  to  have  been  more  or  less  probable 
states  of  the  case.  Thales  is  supposed  to  have  been  born  B.  C.  640,  and  to  have 
traveled  into  Egypt  at  an  early  age,  where  he  learned  astronomy  from  the  priests. 
'Returning  home,  he  probably  applied  this,  and  whatever  other  knowledge  he  may 
have  gained  from  research  and  observation,  to  the  prediction  of  eclipses.  He  may 
have  predicted  many  eclipses  from  B.  C.  610  to  B.  C.  584,  and  longer,  as  he  is  said  to 
have  lived  to  a  great  age.  His  success  in  the  case  of  the  solar  eclipse  B.  C.  584  gave 
him  a  wide  celebrity,  as  we  know  from  the  tables  that  this  eclipse  was  total  at  no 
great  distance  from  his  birthplace.  That  he  predicted  only  a  single  eclipse  is  highly 
improbable;  that,  in  addition,  this  one  should  prove  to  be  total  within  a  hundred  miles 
of  his  birthplace  transcends  all  reasonable  probability. 

Some  time  between  the  dates  we  have  mentioned,  a  battle  was  fought  somewhere 
in  Asia  Minor,  probably  very  tai  ii.'^m  the  home  of  Thales,  in  recounting  which  some 
of  the  participants  expressed  surprise  at  the  suddenness  with  which  it  was  stopped  by 
darkness.  The  story  may  have  passed  through  several  mouths  before  it  reached  any 
one  who  knew  about  Thales,  and  may  have  been  somewhat  exaggerated  in  the  narra- 
tion. At  length,  it  reached  the  ears  of  the  admirers  of  the  philosopher,  who,  recol- 
lecting what  he  was  doing,  and  knowing  that  he  had  predicted  an  eclipse  for  that  very 
year,  seized  upon  the  story  as  a  confirmation  of  the  prediction. 

Who  these  persons  were,  and  in  what  part  of  the  century  which  elapsed  before 
Herodotus  they  lived,  we  can  only  conjecture.  We  can  make  many  hypotheses,  on 
which  the  probability  of  the  correctness  of  the  conclusion  becomes  smaller  and  smaller, 
xmtil  we  approach  the  time  of  the  historian,  when  it  vanishes  entirely.  Under  these 
circumstances,  it  seems  to  me  that  while  the  hypothesis  of  correctness  is  not  an  entirely 
inadmissible  one,  it  rests  on  too  slight  a  foundation  to  be  employed  as  a  basis  for  cor- 
recting the  lunar  tables.  The  rejection  is  farther  justified  by  the  uncertainty  where 
tlio  battle  was  fought,  and  the  considerable  breadth  of  the  shadow,  which  leaves  us  a 
wide  range  for  central  line  of  eclipse.  I  shall  therefore  not  make  any  use  of  the 
eclipse  of  Thales. 

2.— THE  eclipse  at  LAIIISSA. 

The  account  of  this  eclipse,  as  translated  by  Professor  AntY,  is  as  follows : — 

"When  the  Persians  obtained  the  empire  [of  the  east]  from  the  Medes,  the  king 

of  the  Persians  besieged  tliis  city,  but  could  not  in  any  way  take  it.     But  a  cloud 

covered  the  sun  and  caused  it  to  disappear  completely,  till  [i.  e.  to  such  a  degree  that] 

the  inhabitants  withdrew,  and  thus  the  city  was  taken.     Close  to  this  city  was  a  pyra- 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  4,| 

mid  of  stone,  i  plethrum  in  breadth,  2  plethra  in  height  Thence  the  Greeks  proceeded 
6  parasangs,  to  a  great  deserted  castle  by  a  city  called  Mespila,  formerly  inhabited  by 
the  Medes.  The  substructure  of  its  wall  was  of  squared  stone,  abounding  in  shells. 
The  king  of  the  Persians  besieged  it,  but  could  not  take  it.  Zeus,  however,  terrified 
tlie  inhabitants  with  thunderbolts,  and  so  the  city  was  taken." 

Professor  Aihy  adds,  "It  cannot  be  doubted,  I  think,  that  the  disappearance  of 
the  sun  at  Larissa  was  caused  by  a  total  eclipse." 

I  confess  myself  unable  to  share  the  confidence  of  the  Astronomer  Royal  and  of 
Hansen  that  we  have  here  a  total  eclipse  of  the  sun.  The  narratives  of  these  times  con- 
tain many  accounts  of  wonderful  occurrences^in  which  we  know  that  a  liberal  allowance 
is  to  be  made  for  the  flight  of  the  imagination;  and  it  is  not  entirely  logical. to  accept 
unhesitatingly  all  tho?'>  statements  which  we  can  reconcile  with  our  knowledge,  while 
we  reject  all  others.  No  doubt,  if  we  knew  the  day,  or  even  the  year,  of  the  event  * 
described  by  the  historian,  and  found  it  to  be  identical  with  that  of  a  total  eclipse,  we 
should  be  justified  in  accepting  the  coincidence  without  question;  but  as  the  uncer- 
tainty of  date  increases,  the  probability  of  coincidence  becomes  less  and  less.  If,  at  an 
epoch  so  remote,  we  have  a  century  to  find  our  eclipse  in,  we  can  select  any  place  at 
random,  with  a  decided  preponderance  of  chances  in  ftivor  of  our  finding  one  or  more 
eclipses  which,  making  allowance  for  the  uncertainty  of  the  tables,  may  have  been 
total  at  the  point  selected.  It  appears  that  the  Astronomer  Royal  had  a  period  of 
forty  yeai"s  to  find  the  eclipse  in,  and  the  fact  that  one  was  found  in  this  interval  may  be 
considered  as  rendering  the  hypothesis  of  an  eclipse  somewhat  probable.  Notwith- 
standing my  want  of  confidence,  I  conceive  the  pi'obability  of  a  real  eclipse  to  be 
greater  than  in  the  eclipse  of  Thales,  while  we  have  the  great  advantages  that  the 
point  of  occurrence  is  well  defined,  the  shadow  nariow,  and,  if  it  was  an  eclipse  at  all, 
the  circumstance  of  totality  placed  beyond  serious  doubt. 


3.-THE  ECLIPSE  OF  XERXES  (Zkcii,  No.  1). 

( — 477  to  —  480,  spring  of  year.)  ,.  .     ■ 

This  eclipse  occurred  during  the  march  of  Xerxes  against  Greece,  in  the  same 
year  in  which  the  battlo  of  Salamis  was  foiiglit. 

The  descriptions  are  found  in  Herodotus  and  Aristides.  '       '  •" 

From  Herodotus,  vii,  37: — 

"When  the  army,  having  come  out  of  their  Avinterquarters,  in  the  opening  of  the 
spring,  fully  equipped,  set  out  from  Sardis,  for  the  purpose  of  marching  to  Abydos;  and 
when  they  had  begun  their  march,  the  sun,  leaving  his  seat  in  the  li«avens,  was  con- 
cealed from  view,  and  night  instead  of  day  came  on,  though  the  weather  was  not 
cloudy,  but  was  exceedingly  clear." 

From  Aristides,  Scholiast,  ed.  Fkommel,  p.  222  (cpioted  from  Zech,  p.  39): — 

"As  the  king  was  going  against  Greece,  and  had  come  into  the  region  of  the 
Hellespont,  there  happened  an  eclipse  of  the  sun  in  the  east;  for  it  portended  to  him 
his  defeat,  that  the  sun  was  eclipsed  in  the  region  of  its  rising,  since  Xerxes  also  was 
marching  from  the  east." 

If  any  justification  for  entire  want  of  confidence  in  the  eclipse  of  Thales,  and  in 


32 


RESEARCHES  ON  Tl^E  MOTION  OF  THE  NfOON. 


ancient  total  solar  eclipses  j^enerally,  were  required,  it  is  found  in  the  fact  that  this 
description  cannot  be  identified  with  any  total  eclipse  of  the  sun.  Of  all  descriptions 
of  such  eclipses  by  the  Greek  historians,  this  is  the  one  which  is,  all  thin{js  considered, 
most  clear  and  oxidicit.  No  known  natural  occurrence  but  a  total  eclipse  of  the  sun 
could  give  rise  to  the  circumstances  described  by  IIerodotis.  The  place  and  the  sea- 
son are  clearly  specified,  and  the  year  is  one  about  which  I  am  not  aware  that  chro- 
nologists  have  entertained  any  serious  doubt.  The  time  of  day  (morning)  is  obscurely 
indicated  by  the  account  of  Herodotus,  and  clearly  stated  in  that  of  Aristides;  yet  the 
astronomical  tables  seem  to  show  in  the  most  conclusive  manner  that  no  total  eclipse  of 
the  sun  could  have  been  visible  at  Sardis  at  that  time.  I  am  not  aware  that  any  one 
has  given  any  explanation  of  the  occurrence  which  will  reconcile  the  statement  with 
the  tables.  Professor  Airy  considers  the  most  probable  explanation  to  be  that  the 
eclipse  was  not  one  of  the  sun  at  all,  but  that  of  the  moon  which  occurred  B.  C.  479, 
on  the  morning  of  March  14.*  On  this  theory,  the  circumstance  first  to  be  remarked 
is  that  it  is  clearly  incompatible  with  the  narrative.  The  incompatibility  is  explained 
by  Sir  George  by  supposing  that  IlERonoTas  was  mistaken  in  the  single  circumstance 
of  the  eclipse  being  one  of  the  sun,  that  historian  repeatedly  expressing  himself  "doubt- 
fid  on  matters  of  detail  which  occurred  during  the  movements  of  Xerxes  on  the  eastern 
side  of  the  Aegean  sea".  While,  however,  such, a  mistake  as  the  substitution  of  the 
niioon  for  the  sun  is  quite  possible,  it  must  be  admitted  that  the  words  "instead  of  day 
it  became  night"  cannot  be  thus  explained.  Tlie  explanation,  therefore,  how  jn'obable 
soever  it  may  be,  presupposes  so  nuich  play  of  the  imagination  on  the  part  of  the  his- 
torian as  to  render  him  unworthy  of  that  amount  of  confidence  in  matters  of  detail 
which  would  justify  our  changing  the  lunar  tables  to  accord  with  his  statements. 

ZECHt  proposes  yet  another  explanation,  namely,  that  the  eclipse  in  question  was 
that  of — 477,  February  1 6,  which,  according  to  the  tables  of  De  Damoiseau,  was  annular 
at  Sardis.  If  this  were  correct,  it  would  be  necessary  to  change  the  usually  received 
date  of  the  battle  of  Salamis  by  two  years.  The  question  is,  however,  one  of  purely 
chronological  interest,  because,  if  the  eclipse  was  not  total,  no  conclusion  can  be  drawn 
from  it  astronomically.  Tiie  accounts  of  the  historians  do  not  enable  us  to  decide 
whether  the  annulus  was  formed  at  Sardis;  hence  no  conclusion  respecting  the  posi- 
tion of  the  central  line  can  be  drawn. 

4.— THE  ECLirSE  AT  ATHENS. 

(-430,  AugUbt3.) 

The  following  is  the  translation  of  the  description  by  Thucyuioes,  ii,  28: — 
"But  in  the  same  manner,  at  the  new  moon  of  tlie  month, — as  even  in  that  time 
alone  it  seems  to  be  possible  for  the  phenomenon  to  occur, — the  sun  was  eclipsed  after 
midday,  and  having  assumed  a  crescent  form,  some  of  the  stars  having  also  appeared, 
it  again  became  full-orbed." 

From  the  circumstance  that  stars  were  visible,  there  would  seem  to  be  a  consider- 
able probability  that  this  eclipse  was  total.  This  probability  is  lessened  by  the  fact  that 
Thucydides  describes  the  sun  as  having  assumed  only  a  crescent  form,  and  by  the  con- 

*  Philosophical  Transactions,  1853,  p.  199.  "" 

t  Loc.  cit.,  pp.  4c -43. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


33 


sideration  that  it  might  have  been  elsewhere  than  at  Atiiens  that  the  Htars  were  seen. 
Still,  as  the  sun  must  have  been  a  crescent  before  and  after  totality,  I  think  thu  proba- 
bility in  favor  of  the  totality  of  this  eclij)8e  is  as  great  as  in  the  case  of  any  other  of 
those  under  consideration,  though  not  sufficient  to  justify  the  introduction  of  an  equa- 
tion founded  on  it. 

5.— THE  ECLIPSE  OP  ENNUIS. 
(-399.  June  21.) 

This  eclipse  is  introduced  because  some  stress  is  laid  upon  it  by  Hansen.  The 
description  rests  upon  the  following  extract  from  Cicero,  T)e  Itcjjiiblica,  i,  1 6: — "  Ennius 
scribit  anno  CCCL  fere  post  Romam  conditam  Nonis  Junis  soli  luna  obstitit  et  nox." 
The  probability  that  this  ecli})8e  was  total  at  Rome  does  not  seem  sufficiently  great  to 
render  it  worthy  of  farther  consideration.  The  tables  show  that  there  was  a  total 
eclipse  about  the  time  of  sunset;  but  I  see  no  reason  in  the  statement  (juoted  for  assum- 
ing that  totality  occurred  before  sunset,  or  that  there  was  any  total  eclipse  at  all. 

0.-THE  ECLIPSE  OF  AOATHOOLES. 
(-309,  August  14.) 

Of  all  the  ancient  solar  eclipses,  this  is  the  one  of  which  the  totality  may  be  con- 
sidered as  best  established,  and  to  which,  therefore,  we  should  have  least  hesitation  in 
making  the  lunar  tables  conform.  Unfortunately,  there  is  a  doubt  whether  Aoatiio- 
CLE8,  in  his  passage  from  Syracuse  to  Carthage,  went  on  tlie  north  or  tiie  south  side  of 
Sicily.  The  arguments  on  the  two  sides  are  so  evenly  balanced  that  the  question  can 
be  decided  by  the  lunar  tables  alone.  This  renders  the  point  where  the  eclip.se  was 
total  so  uncertain  that  the  eclipse  itself  is  of  little  use.  By  a  singular  fatalit}",  the 
admissible  limits  of  the  position  of  Aoatiioclks  correspond  almost  exactly  to  those  of 
the  limits  of  the  moon's  secular  acceleration.  The  shadow  was  unusually  broad;  and 
between  the  two  extreme  hypotheses,  ( i )  that  Aoatiiocles  was  south  of  Sicily  and  the 
centre  of  the  shadow  south  of  his  position  by  its  semidiameter,  and  (2)  that  he  was 
north  of  the  island  and  the  centre  of  the  shadow  yet  farther  north,  all  intermediate 
ones  are  equally  possible.  While,  therefore,  we  may  be  justified  in  making  it  a  test 
of  the  cori'ectness  of  the  lunar  elements  that  the  computed  shadow  should  fall  between 
these  limits,  we  cannot  determine  those  elements  from  it. 

7.— ECLIPSE  OF  -217,  FEBRUARY  ii. 

I  was  led  to  consider  this  eclipse  from  a  statement  respecting  it  by  Ricciolus,  wiio 
says  {Alnmgestum  Novum,  p.  365),  "Addit  Silius  Italicus  densas  fuisse  &  immensas 
tenebras  in  Calabria  &  subductam  esse  diei  lueem."  But,  on  referring  to  the  original 
authority,  we  find  the  eclipse 'to  become  indefinite.  The  lines  alluded  to  occur  in 
describing  the  wonders  which  preceded  the  battle  of  Cannae  (viii,  634),  and  are: — 

"Quaesivit  Calaber,  subducta  luce  repenle 
Immcnsis  tenebris,  &  terrain  &  litora  Sipus  : 
Obseditqui"  frequens  castrorum  limina  bubo." 

I  find  that  in  this  eclipse  the  central  line  was  far  down  in  Africa,  so  that  it  may 
be  dismissed  with  but  a  single  reflection.     If  so  great  a  misapplication  of  the  words 
of  a  narrator  can  be  made  by  an  astronomer  of  the  seventeenth  century,  what  are  we 
to  expect  of  the  aacient  historians,  and  especially  of  Herodotus  I 
5 75  Ap.  2 


34 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


8.— A.  D.  360,  AUGUST  2^. 

This  iw  No.  16  in  Zkcii's  Imt,  and,  from  tlie  (leHcription  given  by  Am,mianus  Mak- 
(JELLiNua,  would  iippeiir  to  have  been  total  in  Eoos.  But  the  tal)le8  show  the  ecHpso 
to  have  boon  annular,  so  that  we  can  deduce  nothing'  from  it. 

MEDLKVAL  ECLIPSES. 

Boloiigiug  to  the  same  class  with  those  we  have  cited,  but  too  modern  to  be  deci- 
sive of  the  (piostion  of  the  moon's  secular  acceleration,  are  the  eclipse  of  Stiklastad, 
A.  D.  103c,  and  the  total  eclipses  in  which  the  shadow  of  the  moon  passed  over 
Central  Europe  in  the  years  1140  and  1143.  The  last  two  have  been  very  (larefully 
discussed,  and  many  j)oints  at  which  the  eclipse  was  total  determined  from  the  chron- 
icles of  the  times,  by  Cei.oria  of  Milan  in  his  two  papers*  published  in  Memoric  del  It. 
Istituto  Lombardo  di  Scienze  e  Lettere,  vol.  xiii. 

The  preceding  list  includes,  so  far  as  the  writer  is  aware,  all  the  ancient  solar 
ecli[)se8  which  have  been  considered  total  at  any  definite  point  of  i]io  earth's  surt'ace- 
The  general  conclusion  to  which,  we  are  led  is  that  there  is  no  one  of  these  eclipses 
which  we  can  feel  reasonably  confident  was  total  at  a  definite  point.  The  p:'oi)ortion 
of  the  eclipses  which  wo  know  from  the  tables  must  have  been  annular,  or,  at  least, 
which  were  not  total  at  the  points  to  which  they  are  referred,  is  so  great  as  to  destroy 
any  confidence  which  might  have  been  felt  in  tiie  others.  Still,  if  one  value  of  the 
secular  acceleration  should  represent  them  much  better  than  another,  it  cannot  be 
denied  that  this  fact  might  militate  a  little  in  favor  of  that  value  which  1)est  repre- 
sented them.  While  this  ct»nsideration  cannot  aid  us  in  determining  the  value  of  the 
secular  acceleration,  it  may  help  us  in  deciding  which  of  several  competing  values  is 
the  mo.st  probable.  To  enable  the  reader  to  judge  of  the  application  of  this  teat,  I 
arrange  the  eclipses  in  what  seems  to  me  the  order  of  probability  of  totality,  judging 
from  the  narrative  atone,  adding  the  place  where  each  was  supposed  to  be  total 
(i)  Eclipse  of  Agathocles,  —309.     Total  in  or  near  Sicily. 


(2)  Eclipse  of  Xerxes,  —479 1 

(3)  Eclipse,  —430. 

(4)  Eclipse,  -f  360. 

(5)  Eclipse  of  Xenophon,  —556. 

(6)  Eclipse  of  Thales,  —  585. 

(7)  Eclipse, 


Total  at  Sardis. 
Total  at  Athens. 
Total  at  Eoos  I 
Total  at  Larissa. 
Total  in  Asia  Minor. 
Total  in  Sicily. 


+  334- 

Of  these  seven  eclipses,  the  second  cannot  be  identified,  while  the  fourth  and 
seventh  must  have  been  annular.  We  have  therefore  only  four  left  to  test  the  tables. 
Of  these,  the  eclipse  of  Agathoules,  the  only  one  in  ^hich  I  can  regard  the  fact  of 
totality  as  well  made  out,  allows  a  range  of  several  seconds  in  the  secular  acceleration 
The  uncertainty  of  the  remaining  three,  that  at  Athens  in  the  year  — 430,  and  those 
of  Larissa,  and  of  Thales,  has  already  been  discussed.  Altogether,  it  does  not  seem, 
to  me  that  much  light  will  be  thrown  by  these  eclipses  on  the  question  of  the  moon's 
secular  acceleration.  It  seems  to  me  that  the  most  logical  course  is  to  obtain  the  secular 
acceleration  of  the  moon  from  other  data,  and  then  to  undertake  the  discussion  of  the 
historical  evidence  anew. 

•  (I)  SuWEclissi  Solate  Totale  del  3  Gingno  1239. 
(2)  SugliEclissi  Solari  Tetalidtl  3  Oiugno  1239  e  del 6  Otloire  1241. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


15 


TflK  PTOLEMAIC  BOFilPSBS  OP  TRR  MOON  REOORDBD  IN  TFIR  ALMAOEST. 

Tlio  most  comploto  diacusHioii  of  theHO  eclipses  is  that  of  Zkcii,  alroaily  quotod,  in 
whidi,  however,  tlie  treatment  is  such  as  not  to  lead  to  any  definitive  lesnlt.  Zf.cii's  (-(mi- 
parisons  were  made  witli  the  tables  of  De  Damoiskau,  IIanskn's  tables  Ijcinj^  still  nn- 
iinished  when  his  paper  was  pre])ared.  My  general  plan  of  i)roceodin;f  is  this: — From 
the  data  ^\ve>n  by  PTor.KMV,  and  from  his  interpretation  of  the  data,  1  form  what  seems 
to  mo  the  best  judgment  of  the  time  at  which  any  given  phase  was  actually  seen  by  the 
observers,  and  of  the  probable  error  of  this  time,  taking  care  to  do  this  without  any 
knowledge  of  the  way  in  which  the  tabiUar  results  will  come  out.  For  an  epo(;h  near 
this  time,  the  positions  of  the  sun  and  moon  are  computed  from  Hansen's  tables,  and 
thence  the  times  of  the  geometrical  phases  of  the  eclipse.  This  time  is  then  compared 
with  that  observed,  and  an  equation  of  condition  thence  deduced.  In  the  ecjuations, 
the  only  indeterminate  quantities  which  it  is  worth  while  to  include  are  the  moon's 
longitude  and  the  error  of  the  estimate  of  the  phases  of  beginning  and  ending,  arising 
from  the  tact  that  the  eclipse  nmst  have  advanced  past  the  phase  of  beginning  before 
being  sean,  and  must  have  disappeared  before  the  actual  ending 

In  computing  the  places  of  the  moon,  I  have  not  deemed  it  necessary  to  take  into 
account  the  small  terms  which  are  included  in  the  tables  of  double  entry,  as  their 
probable  sum  is  far  below  the  probable  error  of  the  individual  observations.  The 
sum  of  iLo  constants  added  to  these  tables,  or  0.0022240  in  units  of  the  fundamental 
argument,  has,  however,  been  included  with  the  terms,  to  avoid  any  constant  error 
arising  from  this  source. 

The  positions  of  the  places  of  observation — Babylon,  Rhodes,  and  Alexandria — 
have  been  taken  from  Zech,  as  follows: — 

Babylon,  2''  56™  east  from  Greenwich;  latitude,  +32''  15'. 
Rhodes,  i*"  53"  east  from  Greenwich;  latitude, +36°  27'. 
Alexandria,  2''  oo""  east  from  Greenwich;  latitude,  +31°  12'. 

Ptolemy's  descriptions  of  the  several  eclipses  are  as  follows : — 


(0 


Qv  Toivuv  tlX-^ifaiav  ::akaiutv  rpiwv  ixXsiiliswv  h 
iSiv  iv  lla,iuli(ovi  TSTiipij'iijiov,  ij  niv  KpiOTrj  ihayij'pai:- 


"Of  the  three  Jincienteolipses  which  we  have 
taken  frotii  those  observoil  in  B  ibvloii,  tlie  first 
is  recorded  as*  hiivin;;  ouciirred  in  the  tlrst  .year 
Tfli  ytpivula  TO)  iipiiTi/i  cTsi  Map3itxs,uKditiiu,  xar  Alyun-     of  Mardogbupadus,  according  lo  |thH  reckon- 

rioo,(,i>i^x0.l,rii.r.    ///,?ani«,y,^<v,4x-l«W;x£ra    "'8  of  J  the  Egyptians  on  th«  2»th  day  of  the 

month  Thoth,  toward  tlie  3i»th.  It  began  to  bo 
Tijy  lii-aToAiji/,  /jiof  (upai  fxavm?  itaptl^ouarii;,  xa\  i^ili-  gclipsed,  it  is  said,  after  its  rising,  wlien  one  hour 
„cy  SXij,  had  quit«  far  passed,  and  the  eclipse  was  total." 

The  term  iKavoo?  7rape\9ovarfi  seems  to  admit  of  some  latitude  of  interpretation. 
ProLKMY  assumes  the  interval  to  be  an  hour  and  a  half,  IIaktvviq  an  hour  and  a  «|tiar- 
ter.  According  to  Zech,  the  moon  rose  at  5''  53'".  Ptolemy  himself  must  be  considered 
the  best  judge  of  the  somewhat  indefinite  language  used,  and,  on  the  other  hand,  the 
interval  after  moonrise  was  probably  nearer  one  hour  than  two  hours.     I  shall  assume 


36  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

a  m(»an  between  an  hour  and  a  quarter  and  an  hour  and  a  half  as  the  jnoBt  probable 

interval,  nuiking; — 

Habylon  time  ot"  oljscrvod  hof^iuning 7*'   15" 

Correction  for  lonjritude a**  56"' 

Greenwich  mean  time 4**   ig". 

The  prolmblo  error  of  this  ostiinate  I  consider  to  be  12  minutes,  the  interval  of 

time  being  so  short  us  to  admit  of  comparatively  accurate  estimate. 

.  (a) 

//  «  SsuTifia  Tim  Ixktl'i'twv  Avaylyixiittai  ytY"'  "The  Bccoiul  is rficonlod  ns  Imvlng oficnrred 

,      -»      ,      V         ,    ,    -  „    ,         ,,  ,  ,,     in  tlieHecnnd  yeitrof  tliesaiiie  Mardoobmpadus, 

vDi'i  tuii)sutI/iiu  tm  rii'J  aOrim  Miionnxtiinaniiu  xar  At-  •'  ' 

on  the  18th  of  Thoth,  towanl  tb«  19th.    It  was 

roKTiuu^  #<«.•>  ir;  .??  r^.  itf.     E-atTt  Iti,  ,fy,nw,n^o    et'lipsetl  from  the  soiUh  throe  (liKits  in  the  middle 
vdrim  ItaxTuliiuf  rptli  ivjthu  roO  ftiirnvuxTdiu,  of  the  nij;ht." 

The  indefiniteness  of  tlie  time  renders  this  eclipse  of  very  little  value  for  our 
present  purposes. 

The  estimate  of  magnitude  formerly  served  to  determine  the  motion  of  the  moon's 
node,  but  this  can  iii»w  bo  learned  witJi  far  more  accuracy  from  modern  data  So  far 
as  any  indication  ire  given,  the  middle  of  the  eclipse  was  at  midnight,  a  statement  of 
which  the  probable  error  may  be  40  minutes.     We  have,  therefore : — 

Greenwich  apparent  time  of  middle q"*     4™  ±  40'" 

Equation  of  time +  '4'" 

Greenwich  mean  time .     .     g**  1 8", 

(3) 

H  di  Tpkrj  Toiv  lxXt(<ptutv  ivaylypanrai  yiyovuXa  "The  third  is  reuorded  H8  having  ocoiirred 

Toi  alirlfi  itorlfij)  irct  mo  MapSnxs/mdiliiu  xar  Alyui:-  in  t,ii<^  same  Second  year  of  M  A  RDOOBMPADUS,  tlie 

Ti'ouf  taiuvib9  it  tli  tijk  if.     Ilpiarii  di,  ip^tiv,  ixXst-  15th  of  Pharnenoth,  to  vikrd  the  i6th.,    It  began 

izetv  pit4  r-^v  dvaToXijv,  xa)  if^/liiriv  in  Spxrwv  nXtUiv  to  be  ecUpsed,  it  is  said,  after  the  rising,  and  was 

TOO  i)niaou<;,  eclipsed  fy.)ii'  the  north  more  than  the  half." 

The  moon  rose,  according  to  Zkch,  at  6'"  29"  Iroal  time,  or  3''  33"  Greenwich  mean 
time.  We  can  only  conclude,  from  the  data  as  e>  firessed,  that  the  eclipse  had  not 
become  perceptible  at  this  time;  but,  on  the  other  hand,  had  the  interval  been  consid- 
erable, say  one  hour  or  more,  it  would  probably  have  been  described.  Pror.BMV  sup- 
poses the  interval  half  an  hour  I  shall  assume  it  to  be  25  minutes,  with  a  probable 
error  of  20  minutes,  which  will  make  the  • 

Greenwich  mean  time       s""  58"  rfc  20™. 

(4)     —620,  April  21. 

^a  yAp  niftKTw  irt:  Sa^uitoUaadpm,  8  iauv  pit"  "  In  the  fifth  year  of  NABOPOLA8SAB,  wbich 

<4|P  .  ,      -  is  the  127th  year  from  Xabomassab  according  to 

fr,;?^;rd  Na^».aa«Ap,m,  xar  Alyonrioo,  Aoo    xC  ti,    ^^^  Egyptian  reckoning,  on  the  27th  of  Athyr.to- 

T^v  xTj  &pa<;  ta  Xr/youarit,  iv  Ba^uXtovi  ^p^ato  7  (TsXyji^ii  ward  the  28th,  at  the  closing  of  the  eleventh  hour 

.  ,  ,           .   ■  „         ,     ,           ,  ,    ,       -        .  in  Babylon,  the  moon  began  to  be  eclipsed,  and 

'                                                       '  was  eclipsed  mostly  on  the  south  a  fourth  of  the 

itiTpou.                                                                .  diameter." 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  37 

• 

The  timejiere  indicated  in  55  minutes  before  sunrise,  which  occurred  nt  17''  36"' 
local  apparent  time,  or  tlie  h»cul  niuiin  time  of  boginnin^f  is  16''  ^j"',  the  efiuatioii  of 
time  being —4'";  and  the  (iroenwidi  mean  time  13'' 41"".  Tlie  probaldo  error  may 
be  estimated  at  15  minutes. 

* 

(5)    -522,  July  i6. 

lldXtv  Hi,  T#  c»  't«i  Ka/ifioauu,  8  iffT(  a,i"  ft,,,-  "  I"  the  seventh  .yfiir  o»  (Jamhyskh,  which 

U  the  a25th  yeiir  I'loiii  Naiionassak,  nccording 
ini  IVaflovaaadpou,  tar  Al/urTT{.ui  tatit\>d>»  i:  tli  Tijv     t„  t|,„   K(,'.V|>tiails,  Oil   the    17th  of   I'hHineiloth, 

-      ,     ,    „  .  /      1    I,  o  ,-    iSYi  towuid  the  18th,  one  hour  before  inidiiiKht  in 

'    '    '^        '  liiihyloii,  the  inooii  wiw  eclipsed  from  the  north 

ij  atXrjvri  dit"  SpxTiuv  ri  (j/itiro  riff  HutnlTpim.  one  hiilf  of  h«^r  diameter." 

We  have  then  : — 

Estimated  local  apparent  time  of  middle  of  eclipse     .     1 1""  10™ 

Equation  of  time —     i"' 

Greenwich  mean  time S**  13"  ±  24™. 

A  large  uncertainty  of  phase  is  to  be  added  to  the  probable  error. 

(6)     —  501,  November  19. 
Jturipa'/tk, >••""•  "The  second  eclipse  happened  in  the  20th 

Hivj)  Tipx  irtt  Japtluu  Tim  /itrd  Katt^oarjv,  xar  Aiyor.-     year  of  DARIUS,  successor  of  CaMBYBBS,  Oil  the 

T("u?  E^iip\  %i)  ik  Tijv  xfl,  rryf  mxTix  npotXOouarji  t<tr,-  28tli  of  Bpiplii,  towurd  the  29th,  theuight  having 
ntpt\iAii;mpa<;<:/,itaif^v6ii(>(ii":iHXnftv^atX'^^yi  ani  advanced  64  equinoctial  hours,  the  moon  was 
v6roo  Ti  sr  T^z  Sianhpou,    .....  n  lipsed  on  the  south  J  of  her  dia;ineter.'' 

The  sun  set  at  5*"  11"'  apparent  time;  the  equation  of  time  being  —  13°.     The 
mean  time  here  indicated  is  11''  iS™,  and  the  result  is : — 

Greenwich  mean  time  of  middle  of  eclipse       .     .     .     .     8**  22"°  ±  25"'. 

(7)     -490,  April  25. 


FMiSo/itv  tij  itpd>Ti,i/  /ih  ixketifiiv  Tijf  M  Japtlnu 
Tim  npi&Tim  Ttrij/Jij/i^Kryw  iv  Ba/3uXu)v:  rip  itpdrip  xa\ 
Tptaxiiirrip  iiliTim  tret,  xar  AlyuKTiim^  To^i  y  ik  t^v  d, 
iupiif  1;  nimji,  xaff7)v  StanaiftUai  in  i^iXtiittv  ij  atXijvri 
iXnti  vnxHO  itaxTuXou^  /S. 


"  We  have  taken  an  eclii)8e  observed  in  the 
time  of  Darius  the  first  in  Babylon,  in  his  3i8t 
year,  on  the  3d,  toward  the  4th  of  Tybi,  in  which 
it  is  shown  th<it  in  the  middle  of  the  sixth  hour 
the  moon  was  eclipsed  two  digits  on  the  south." 


The  local  apparent  time  here  indicated  is  1 1*"  28",  the  equation  of  time  —5",  the 
Greenwich  mean  time  8''  27"";  probable  error,  25  minutes. 


(8)     —  382,  December  22. 

.     .     .     .    ytyiivlvat  m  T-ii^  T:p(lnT,v  &px»vTiii  AO-^vjtai  "  Phanostrateb  being  archon  at  ..VtbttUS, 

favoarpiiTuo,  n^v6i  nnastSsmvo;,  xai  hXeXiitizivai  rr,v  the  inooii  WHS  eclipsed  at  Babylon  in  a  siiia!!  i'.ait 

atX^vT,-^  fipaxb  nlpo^  nm  xi>xX<m,  ind  Oepv^f,^  dvan/^^?,  of  her  orb,  ou  the  side  of  the  sUinmer  rising,  when 

T??  vuxxii  XiHKim  Svroi  ^niiupiim.    Ka\  en,  ipt,ah,  ix-  one  half  houf  of  the  uight  was  still  remaining,  and 

Xthtouaa  idu.  tho  moon  was  still  eclipsed  when  it  set." 


38  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

The  first  time  here  indicated  is  36  minutes  before  snnrife,  or  iS*"  28"  local  apjiar- 
eiit  time,  and  18''  31'"  mean  time.     We  have,  therefore: — 

Greenwich  mean  time  of  a  small  ecHpse 15'' 35™  ±10'". 

(9)     —381,  June  18. 
ild>.tv  TTjv  iz^j  txXtnl'iv  iprjai  ytymivai  apj^mTiii;  "Phanostkatks  buing  aroliou  at  Arbens, 

/<i)>)vi;(r!  0a/i)(jTpaTiii),  H^xt/KKfii/nwxi;  /i7jvA(;,  xar  A'.yun-     Oil  tlu*  24th  of  PliailieilOtll,  tOWttnl  the  2Sth,  it  was 

Ti'iioj  i?s  «Pa/i£v(«tf  X'!  £!?  T>/i  z£.     E'ihnt  ili  ^Tjittv  a^iu  said  to  be  eclipsed  Oil  HUininer  rising  [at  Baby- 

ftspivti^  ayaritXiii  rfi^  T:iio'Trii  wjia- zfiiishikuOuia^.  .  ,  ,  loll  |,  the   Brst   liouF  being   passed.    The  whole 

AW  i!cs\  V  j:!:;  -^pirj };  Ti}i  ixksi  "iiu;  topS)/  rpiiov  duu-  duFcttioii   of    the  uulipsu    is   recorded   as  three 

YpdfSTai, hours." 

The  date  is  —381,  June  18.     The  sun  set  at  7''  3™  apparent  time,  or  6''  57™  mean 
time.     The  interval  mentioned  may  be  roughly  estimated  as  somethino-  more  than  one 
equinoctial  hour,  say  i  hour  and  7  minutes,  with  a  probable  error  of  10  minutes. 
We  have,  therefoi  e : — 

Local  mean  time  [of  beginning  (?)] S*"  4"" 

Greenwich  mean  time  [of  beginning  (I)] i     .     .     5''  8™ 

Greenwich  mean  time  of -ind 8'' 8"'. 

(10)     — 381,  December  12,  Babylon. 

I'.^ikits  W,  tpTftnvy  SXt)  dp^apivri  dftu  Ssptwuiv  fli/«-  ''It  was  said  to  be  totally  eclipsed,  having 

T,Mv  d  wpwv  napeHijXu»uiiov.  begun  On  the  summer  rising,  four  hoiirs  hiiving 

gone  by." 

The  sun's  semi-diurnj'l  a'-c  at  Babylon  was  5''  5",  the  length  of  the  temporary 
hour  was  nearly  i''  10'"  ,  the  four  temporary  hours  would  have  been  nearly  4  hours 
40  n'.inutes;  and  as  they  had  already  passed,  we  may  estimate  the  probable  time  at 
4''  50'"' after  sunset,  with  a  probable  eiTor  of  24  minutes.  The  equation  of  tine  being 
—  3"',  we  have  : — 

Local  mean  time  of  beginning 9"  52" 

Greenwich  mean  time  of  beginning 6''  56™. 

(11)     —200,  September  22. 

xfiO' Tjv  iip^aro  !iiv  hhtKstv  "The  uionn  began  to  be  eclipsed,  on  the  one 

ij  (T£/i)jvij  irpd  ■qiittopiiiii  T^?  dmriikii^,  erTjiuTiiv  Ss  dvsKkrj-     hand,  half  all  lioup  befo"<'-  the  rising,  but  was 
ptuft,,  rpirr/;  aipai  iiiirr/^.  tilled  Up  again  ill  the  middle  of  the  third  hour." 

If  IIu'i'ARCniTs  is  here  fully  and  correctly  quoted,  which  is  very  doubtful,  he  must 
have  had  a  very  indefinite  idea  of  the  difference  between  a  calculated  and  an  observed 
phenomenon,  speaking  as  he  does  of  an  eclipse  commencing  half  an  iiour  before  it  was 
[lost  ible  for  the  moon  to  be  seen.  Still,  as  the  half  hour  is  probably  the  result  of  an 
estimate  from  the  magnitude  of  the  eclipse  at  the  time  the  moon  first  became  visible, 
it  is  not  without  value.  The  moon  rose  at  6''  o'"  apparent  time,  which  was  5''  53"" 
mean  time.  Tlie  middle  of  the  third  hour  was  about  S""  32'"  apparent  time,  or  8''  25"" 
mean  time,  making  the  Greanwich  mean  time  of  ending  6''  25'"  ±  (2™. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  39 

(12)     — 199,  March  19,  Alexandria. 

Ilfiiaro  'U  Tfi<;  mxri)^  irpnsXeouawv  w/iBv  e  xa't  "It  began  .vlieii  5J  houra  of  the  night  were 

Tpnij/w/iiou,  xa\  i^iXiKtv  o/ij.  pa88e«l,  and  it  wa.s  total." 

This  is  11''  19'"  apparent  time,  11''  29"'  local  mean  time,  and  9''  29"°  Greenwich 
mean  time.  • 

(13)     —  199,  September  11,  Alexandria. 

///(JUT"  <5c  T/;?  wjxroc  T/v.Ufl-yffwviu/Kui-T;-;,, z«!  "It  began  6§  hours  of  the  night  having 

iU^-iJ^sv  okij.    h'ai  rdv  ;i.lti>v  'U  r/)?  huivstu^  -^imvuv    passed,  and  it  was  total,  and  tlie  middle  of  the 
V,^!  r'T">''""  '^/-^  ^r"-^  !"''■''■"''"  ^  "'^  rinrrnLopu,:,    eclipse  arrived,  he  saya  about  8^  hours  of  the 

night." 

Here  we  have  again,  in  the  "middle  of  the  eclipse",  a  time  given  which  it  was 
impossible  to  observe,  withont  any  indication  of  the  data  from  which  the  time  was 
derived.  As  the  eclipse  was  total,  the  most  natm-al  data  would  have  been  the  ob- 
served times  of  beginning  and  end  of  totality,  which  would  be  far  more  accurate  than 
tlie  observed  times  of  beginning  and  ending  of  the  partial  phase.  The  times  indi- 
cated are: — 

Local  apparent  times  .     .........     12"  41'"  «"tl  14"  25'" 

Local  mean  times 12"  38'"  and  14"  22™ 

Greenwich  mean  times 10'' 38"  and  12  '  22'". 

(14)     —  1 73,  April  30,  Alexandria. 

•/•,5  r,n.u.  C.  ?r.,   1>0..,nrop..,,  o  .Vr,  y,»5o^  a.i  "  I"  the  ^l\^  year  of  PniLOMETER,  which  iS 

tlie  S74tli  from  Nabonassau,  on  the  27111  of  I'ha- 
Sa{ ovaaadpuu,  xar  AlyoKTliit,:;  <P>i;ii'Mo/t  zC  £lj  rr^v  xji,     meuoth,  towar(i  the  28th,  tlie  inoon  was  eclipsed 

,      in  Alexandria  from  the  beginning  of  the  eighth 

i;i)^t'rs>' ij  (rsX^vTj  TO  TsXtiaziiv  a-"  llpxrim  Saxrui.oui  :;.        north,  SCVen  digits."  ,         '    ^ 

These  times  are : — 

Local  apparent  tines 12"  54"  and  is""  37"" 

Local  mean  times 12"  48"  and  15^  31" 

Greenwich  mean  times 10'' 48'"  and  13' 31'". 

(15)     —140,  January  27,  Rhodes. 

Ildh.   <1r,  r^i  Xy    k'r^'  rr];  rphr,-  xazA  hnU::-.^  "...     the  607th  year  from  NABONASSAU 

^tpM.o,  5  i.TTiv  xl  «Td  Na,io,aaadp„u.  xar  Alru-riat  -  [Eg-VPtin"  reekoiiiiigl,  the  second  of  Ty  ..i  toward 

7«,3)  J  d;  T^v  r,  <J/'«>  ^  «/'Z"/'^"i--,  ^•-'  /'"'V  i"'"'"  tli«  third,  at  tlie  beginning  of  the  stli   hour  in 

{xLiK.r.  ii  .rUi^v  xa-i  l,:,ax„r^^  rd  7rAc-r<rr.,v  «;:«  v.'.rao  Uliodes,  the  moon  bcgiUl  to  be  eclipsed,  and  was 

r?«x7fJA«uf  r.  obscured,  mostly  ou  the  south,  three  digits." 

This  is  9"  42™  local  apparent  tims,  lo"  o™  mean  time,  and  8"  7"  Greenwich  mean 
time. 


40 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Jturipav  3i  rijv  TiTTjpriiUvqv  iv  AXs^aviSpeif,  tu5 
0  tTSi  ASfjtai>ouj  xaT  AlyOTTTiou;  llaymv  tX  ei>  tt/v  oj, 
jT/oi)  Tpimv  wpiuv  ltn)ntpi)imv  xa\  rpimv  rl/iJtrwv  /ndj  &paj 
Tii'j  usaiivuxTiDUf  xaO'  t)v  6/tinioi  i^iXenrsv  ij  aeXijvi^  rd 
IxTiiv  fxipo^  T^f  tia/jLiTpou  ii:i  nearj/iPplaj, 


(i6)     125,  Ain'il  5,  Alexandria.  "  • 

"On  the  lytb  of  Paclion,  toward  the  i8th, 
3I  equinoctial  hours  before  midnight,  the  moon 
was  eclipsed  the  sixth  part  of  her  diameter  on 
the  south." 


This  is  8''  24™  apparent  time,  8"  26™  meaa  time,  and  6''  26'"  Greenwich  mar 


time. 


(17)      ^33,  May  6,  Alexandria. 


lldXtv  wv  eiX7l<pa/isv  rpmv  ixXsOiieutv  ix  rmv  kit:-  "  Of  the  three  eclipses  whioli  we  have  taken 

iitXiaraTa  ijitXv  iv  AXe^avdpua  TeTTjprjiiiviovj  7  /xiw  irpwrrj     from  tliose  Very  carefully  Observed  by  US  in  Alex- 


yiftivs  Tip  tl  sTst  A&piavDo,  xar  AiyuKTi^u^  llaiivt  x  si; 
TfjV  xa,  Tuv  Si  iiiaov  jfpiivov  dxpiiSw;  ir:sX<i)'tiTd;is9it 
yc/ii/ijat  npu  ijniaiiui  xai  Tsrd/Kini  /naj  (upa^  liri^nspi/rj!; 
Tir)  ,nstTovuxT{uu^  xal  l^iXfrcv  SXrj,  xa(f  riv  aipav  dxptjiius 
iittT)[i^  6  ijXtui  Tuu  rai'tpuu  niitpa;  ty  <S"  iyytara. 


andria,  the  first  occurred  in  the  77th  year  of  Ha- 
DiiiAN,on  the  2otli  of  Payni,  toward  the  ztst.  We 
accurately  noted  the  mid  time  to  have  been  one 
half  and  one  fourth  of  au  equinoctial  hour  before 
midnight,  and  it  was  wholly  eclipsed." 


The  apparent  precision  with  which  the  time  is  here  expres.sed  tends  to  inspire 
confide  .  j,  although  we  still  have  no  data  respecting  tiie  manner  in  which  it  was  de- 
termined. The  apparent  time  being  1 1''  1 5'",  the  local  mean  time  is  11''  8'",  the  Green- 
wich mean  time  g""  8"'. 

(il)     134,  October  20,  Alexandria. 


//  8i   StuTipa  yiyuvs   rip   ill  eret    A/tptavvti  xar 
Alyuirriout  Xo'idx  jS   sli  rijv  y,      Tiv   !tk  jiiaov  ^povov 


"The  second  occurred  in  the  19th  year  of 
UA.UBIAN,  the  2d  of  Ohu'iac  toward  the  3d:  the 


raid  time  we  noted  to  have  been  one  equinoctial 
lKsX„ytad!u,%i  ytyinhai  rtpS  a  &pa;  lar,iicpMt<:  r»D    |,„nr  before  midnight,  and  it  was  eclipsed  on  the 

ixsamuxr'iiu,  north  one  third  of  the  diameter." 

1 1*"  apparent  time  is  here  lo*"  46'"  mean  time,  and  S""  46™  Greenwich  mean  time. 


(19)      136,  March  5,  Alexandria. 


//  5k  rphr/  raiv  IxXciil'euiv  yiyovs  roi  x  trci  AHpta- 
vou  XUT  AlyuKTiDUi  <Papijii)U>yi  tO  £l<;  Tj/V  x,  Tiv  iti  iii- 
aov jfpovdv  ineXoyiad/xeiia  yeyovimt  /itrd  i5  mpa^  lirr/iis- 
pi.vd^  Tou  iisaiivuxTiDU'  xal  i^iXint  rd  Tjiitno  T^f  itia/ti- 
Tptio  dr  apxTiov, 


"The  third  eclipse  happened  in  the  20th 
year  of  Hadrian,  on  the  tgth  of.Pharmouthi, 
toward  the  20th  :  the  mid-time  we  noted  to  have 
been  four  equinoctial  hours  after  midnight,  and 
it  was  eclipsed  the  half  of  it«  diameter  on  the 
north." 


le"*  apparent  time  was  then   iG*"  14"'  meantime,  and   14"  14"  Greenwich  mean 


time. 


RESEARCHES  ON  TIIK  MOTION  OF  THE  MOON. 


41 


Tills  completes  tlio  scries  iis  given  by  Ttolemv.  The  tiihul.-u-  positidiis  of  the  sun 
jindnioon  derived  from  Hansen's  tables  for  epochs  of  Greenwich  mean  time  near  the 
observed  phases  are  shown  in  the  following  table.  These  places  have  all  been  com- 
pnted  in  duplicate,  the  two  computations  being  made  by  two  separate  computers.  The 
motions  in  longitude  are  for  0.0 1  of  a  day,  as  the  tiibles  most  conveniently  give  them. 
The  motion  in  latitude  is  supposed  to  be  ,\  that  in  longitude,  positive  at  the  ascending 
and  negative  at  the  descending  node.  The  node  can  be  identified  by  the  value  of 
f-\-  a),  which  is  the  *ngular  distance  of  the  moon  past  the  ascending  node. 

It  may  be  remarked  that  the  probable  error  of  the  longitude  arising  from  the 
omission  of  the  terms  in  the  tables  of  double  entry  is  about  24". 


Tabular  Data  for  Eclipses  of  the  Almagest. 


No.  of 
Hcli|>sc. 

I 

Dale. 

—  720,  Mar.  11) 

Cr.  M.  T. 
of  Com- 
putation. 

Moon's 
Longitude. 

14.4/' 

Motion  in 

cy'.oi. 

IT 

J'arallui. 

Uuituile. 

/.- 

(D's  I.onp. 

(•>'s 
Seinitliam. 

■4.4  A' 
Motion  in 

0.60 

h    m 
5    0 

■7"    59.3 

7-37 

/■  ■ 
55-7 

0        / 
+  0      3.6 

0.5 

0 
351 

1 

3'-5 

15 

57 

" 

—  719,  Mar.    8 

8    0 

160    30.4 

7.10 

53-9 

+  0    46.7 

8.3 

340 

41.8 

16 

0 

0.60 

.1 

—  719,  Sept.    1 

3    0 

yst   55.4 

9.08 

61.2 

-  0    37.8 

187.6 

ISO 

54'4 

16 

0 

o.j8 

4 

—  6ao,  Apr.  21 

13     Q 

204    id. 2 

7.11 

54.0 

+  0    52.8 

169.8 

34 

23.S 

IS 

49 

0.59 

5 

-  52a,  July  iC 

8    o 

286    37:2 

7. .8 

S4» 

-  0    40.9 

352.3 

106 

33. a 

15 

48 

0.57 

6 

—  501,  Nov.  19 

8     a 

51    41.8 

7.08 

53.8 

+  0    50.7 

170.3 

231 

54-2 

16 

16 

0.60 

7 

-  490,  Apr.  25 

7    0 

207    55-8 

8.13 

57-8 

+  I      1.6 

168. 1 

28 

3'-4 

'5 

49 

0.59 

8 

-  382,  Dec.  22 

16    0 

B6    46.9 

8.72 

59-9 

-  0    57.8 

348.7 

367 

2.0 

16 

•7 

0.61 

5 

—  381,  June  18 

4    0 

259    47.0 

7-'7 

54-3 

+  0    46.5 

171. 3 

80 

27.8 

15 

45 

0.57 

ID 

—  381,  Dec,  12 

6    0 

75     "-8 

9-'4 

61.3 

—  0    21.2 

356.0 

356 

9-9 

16 

17 

0.61 

II 

-  200,  Sept.  22 

5    0 

336    20.4 

7.48 

5S.4 

+  0    33-4 

>73.8 

176 

0.7 

16 

4 

0.59 

13 

—  199,  Mar.  19 

8    0 

173     56-4 

8.28 

58.3 

+  0      4.9 

0.9 

355 

32. 4 

15 

58 

0.59 

>} 

-  199,  Sept.  ti 

10    0 

343    55. ' 

8.33 

58.5 

+  0      0.1 

180.3 

X65 

■  ■7 

16 

I 

0.58 

M 
'5 

-  «73.  Apr.  30 

—  140,  Jan.  27 

10    0 
b     a 

214    45-9 
123    26.4 

9.07 
9.14 

61.  J 

61.3 

-  0    35.7 
+  0    46.6 

186.8 
8.9 

35 
304 

40.1 
3'.9 

'5 
16 

49 

13 

0.57 

0.60 

16 

+  125,  Apr.    5 

6     0 

194      2.6 

8.3. 

58.4 

+  0    57.4 

168.8 

'4^ 

16.2 

"5 

54 

0.59 

>7 
18 

+  133.  May    6 
4-  134,  Oct.  20 

.3    0 
8    0 

223    56.1 
25    64. 9 

7-33 

7.56 

54-8 
55.7 

-  0    ■'SI 

-  0    36.8 

355  •• 

18s. 3 

44' 
306 

11.5 
15.1 

■5 
16 

48 

tl 

0.58 

0.60 

>9 

+  136,  Mar.   5 

12    0 

163    5>-8 

8.89 

60.5 

-  0    53.3 

349-7 

344 

36.9 

16 

3 

0.60 

Owing  to  the  somewhat  indefinite  character  of  the  data  given  by  Ptolemy,  it  will 
'.!!•: t  the  judgment  to  present  both  his  statements  and  the  tabular  results  in  a  form  in 
.v.iicV  they  can  be  best  compared.  This  is  done  in  the  following  table,  from  which 
the  reader  can  obtain  a  clear  view  of  the  comparison.  The  deduction  of  the  numbers 
in  the  third  and  fourth  columns  has  been  given  with  the  separate  descriptions  of  the 
eclipses.  They  therefore  need  only  these  two  remarks:  (i)  that  the  probable  errors 
are  the  result  of  judgment  from  the  terms  of  the  description  rather  than  of  calcula- 
tion; (2)  that  they  were  estimated  without  any  knowledge  of  the  way  the  comparison 
with  theory  would  come  out,  and  are  printed  without  subsequent  alteration. 

In  the  column  of  "Phase  described",  A  means  magnitude  of  the  ecUpse.  The 
tabuhir  time  of  geometrical  phase  gives  the  time  of  beginning,  middle,  or  end,  as  the 
'uiso  may  be.  The  quantities  A,  and  As  in  the  last  column  represent  respectively 
the  number  of  minutes  a  central  eclipse  may  be  supposed  to  have  advanced  before  the 
observers  would  see  it,  and  the  immbor  of  minutes  before  the  end  that  the  observers 
From  eclipses  (9),  (13),  and  (14),  the  only  ones  of  which  both  beginning 
75  Ap.  2    ■  . 


lost  sight  of  it. 


4= 


RKSKARCIIKS  ON    IIIK  MOTION  OK  Tllli  MOON. 


1111(1  011(1  were  oliservcid,  A,  -f-  A.j  ooiiios  out —  lo"'.     But,  tliny  niust  both  be  positive, 
and  tliis  result  only  iiuliciitu.s  that  they  are  very  small.     I  shall  put  coiijecturally 

A,  =  3"' 
Aazr  a™. 


(Jrccnwicli 

No.  of 
Eclipse. 

Dale. 

Mean  Tunc, 

iiulicated  hy 

Proi.KMY. 

Prob. 
Error. 

HI 

Phase 

ilescribcd  by 

Plol.KMY. 

Tabular 
Duration. 

Tabular  Time 

of  Gcomct. 

Phase. 

Coir,  to  Tabular 
Time. 

//    ni 

■ 

A 

/(     III 

m 

I 

—  720,  M.-ir.  19 

4     19 

12 

Beginning    . 

3.8 

4     II 

+      8  —   I .  OA 

2 

—  7lg,  Mar.     S 

9     .3 

Middle  (?)     . 

1.9 

8     15 

+  63 

3 

-  7'9.  Scpl.    I 

3     58 

■2 

•    ing    • 

a-4 

3     15 

+  43  -  i-i^i 

4 

—  620,  .\pr.  21 

13     41 

15 

'          ling   . 

I.O 

12     57 

+  44  -  3-8.il 

5 

—  522,  July   If) 

8     >3 

24 

*...      .le   (?)» 

2.6 

8      0 

+   >3 

6 

—  501,  Nov.  i(j 

8     22 

24 

(  Middle   (?■■  ) 

■    I.I 

8    27 

-     5 

7 

-  4<)0,  Apr.  25 

3     27 

*4 

(  y      .ie    (?)  ) 

0.6 

8     17 

H-   10 

a 

—  3R2,  Dec.  22 

15     35 

10 

Small  eclipse 
(connnciic'g). 

1.6 

i5     52 

-    17  -  2.2A, 

1 

9 

-    3Si,Jmic  18 

5       S 

12 

Hoginning    . 

2.4 

4     25 

+  43  -  I.5.ii     1 

s     s 

20 

End   .      .      . 

2.4 

b     51 

+  77  +  J -5^2 

10 

-  3S1,  Dec.  12 

5     56 

24 

Beginning    . 

3-4 

5     57 

4-  59  -  i.ia, 

II 

—  2ix),  Sept.  22 

3     23 

30 

Begin,  (est.). 

3.0 

2     57 

4-  26 

6     25 

12 

End   .     .     . 

.    . 

5     55 

+  30  +  I .  saj 

13 

—  ig(),  Mar.  19 

9     29 

15 

Beginning    . 

3.6 

8     51 

+   38  —  I.Oi, 

"3 

—  199,  Sept.  11 

10    33 

18 

Beginning    . 

3.6 

10     13 

+    25    -   I. Oil, 

12      22 

20 

Middle    .     . 

12       3 

+   '9 

!        U 

-  173,  Apr.  30 

10     4S 

20 

Beginning    , 

2.7 

10      4 

+  44  -  1.4^1 

13      31 

20 

End  .     ,     . 

.    . 

12     45 

+  46  +  i.4;ij 

15* 

—  140,  Jan.   27 

8       7 

20 

Beginning   . 

1.9 

6    44 

+    83   —    2. Oil 

i       l6 

+  125,  Apr.     5 

6     26 

iS 

(Middle   (?)| 
1       ^=.'i        f 

1.2 

6     36 

—   10 

>7 

+  133,  May     0 

9       8 

13 

Middle    .     . 

3-5 

8    38 

+  30 

^       .3 

+  134,  Oct.    20 

8     46 

»5 

Middle    .     . 

3-3 

8    33 

+  »3 

i       "> 

+  136,  Mar.    5 

14     14 

15 

Middle    .     . 

3.2 

13    26 

+  48 

We  shall  now  consider,  seriatim,  the  conclusions  that  we  may  draw  from  the 
comparison. 

1.  The  discordances  of  the  times  in  the  last  column  are,  on  the  whole,  not  mate- 
rially greater  than  would  result  from  the  probable  errors  in  the  fourth  column.  We 
therefore  conclude  that  the  probable  errors  have  not  been  vinderestimated  to  any 
great  extent. 

2.  There  are  five  eclipses,  namely,  Nos.  (2),  (5),  (6),  (7),  and  (16),  in  which  the 
])haso  is  not  expressly  stated  by  Ptolemy,  but  in  which  the  middle  of  the  eclipse  has 
hitherto  been  supposed  to  be  referred  to.  Hut,  in  the  case  of  at  least  the  last  three, 
the  tabular  comparisons  give  color  to  the  suspicion  that  it  was  really  the  time  of 
beginning  which  was  noted;  and  this  suspicion  is  strengthened  by  the  consideration 
that  it  was  the  time  of  beginning  which  was  generally  noted  by  the  predecessora  of 

*  Zkch  supposes  an  error  of  an  hour  in  the  time  of  this  eclipse..  The  alter.-ition  does  not  seem  to  me  justified  by 
t'rj  Jiscordincc  of  two  and  a  half  times  the  probable  error. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


43 


Ptolemy.  I  therefore  deem  it  advisable  to  reject  these  five  ecHpses,  owing  to  the 
uncertainty  of  the  phase  noted.  Quite  accordant  results  might  be  obtained  by  sup- 
posing that  the  beginning  was  observed  in  some  cases  and  the  end  in  others ;  but  the 
uncertainty  is  too  great  to  justify  this  course. 

3.  Tlie  question  whether  eclipse  No.  (8)  was  really  seen  is  a  very  serious  giie.  When 
we  take  out  the  five  doubtful  eclipses  and  this  one,  seventeen  observations  of  phase 
are  left,  every  one  of  which  indicates  a  positive  correction  to  the  tabular  time ;  and 
the  results  throughout  the  nine  centuries  over  which  the  records  extend  are  so  accftrd- 
ant  that  I  do  not  see  how  the  reality  of  this  correction  can  be  doubted.  The  serious 
])oint  is  not  simply  that  No.  (8)  gives  a  negative  result,  for  this  might  arise  from  acci- 
dental errors  of  observation,  but  that  a  positive  correction  to  the  time  will  render  the 
eclipse  absolutely  invisible  at  Babylon.  In  fact,  the  account  says  that  there  was  a 
small  eclipse  (not  simply  that  the  eclipse  was  beginning)  half  an  hoitr  before  sunrise. 
At  this  time,  however,  the  twilight  would  liave  been  .so  bright  and  the  altitude  of  the 
moon  so  low  that  the  eclipse  could  not  be  seen  for  a  number  of  minutes  after  its  com- 
mencement. On  the  other  hand,  the  tabular  time  indicates  that  tlie  ecli})se  did  not 
commence  geometrically  until  about  nineteen  minutes  before  sunrise;  and,  in  this  case, 
the  eclipse  could  scarcely  have  been  seen  at  all,  because  the  constantly  increasing 
light  and  the  constantly  diminishing  altitude  of  the  moon  would  have  drowned  out 
the  slowly  increasing  eclip.se.  In  fact,  when  the  sun  rose,  the  moon  would  have  been 
eclipsed  only  about  3',  or  one  tenth  of  her  diameter.  If,  again,  we  take  the  tabular 
coiTcction  indicated  by  the  other  eclipses,  we  find  that  the  eclipse  did  not  begin  until 
some  time  after  the  moon  had  set. 

We  have  therefore  this  dilennna:  either  there  is  a  mistake  aljout  the  eclipse 
of  —382,  December  22,  having  been  really  observed  at  Babylon,  or  the  seventeen 
good  observations  of  phases  cited  b)'  I'toi.emy  are  systematicall}'  in  error  by  nearly 
half  an  hour.  I  cannot  hesitate  in  accepting  the  former  as  the  most  probable  alterna- 
tive. The  occurrence  of  the  eclipse  being  expected,  it  is  quite  possible  that  the 
observers  may  have  thought  they  saw  the  moon  eclipsed  in  the  increasing  daylight, 
when  there  was  really  no  eclipse;  or,  uiuler  tiiC  unfavorable  circumstances,  they 
might  have  been  deceived  by  a  dark  region  of  the  lunar  disk  being  near  the  moon's 
lind).  Nor  can  a  mistake  of  date  be  regai-ded  as  out  of  the  question.  On  the  whole, 
I  think  that  this  eclipse  shoidd  be  rejected,  since,  if  we  regard  it  as  a  real  observation, 
the  results  from  the  other  eclipses  nmst  be  regarded  as  all  wrong. 

We  have  left  thirteen  eclipses,  of  four  of  which  two  phases,  beginning  and  end, 
were  observed  or  estimated.  Wo  next  divide  these  into  groujjs,  and  take  the  mean 
by  weights,  derived  approximately  from  the  probable  errors  in  the  fourth  cohnun. 

From  eclipses  (i),  (3),  and  (4),  giving  them  the  respective  weights  3,  i,  and  2, 

we  find : — 

Epoch  -  68;,  ^r=  +  26'"  -  2.0  ^i  =  +  20"' ±  8'". 

From  (9)  and  (10),  Avith  the  weights  8,  3,  and  2,  we  find: — 

Epoch  -  38I,  ^T=  +  53"' -  1 . 1 -/.  +  0.3 -'.J  =  50'"  ±  Q" 

From  (11)  to  (15)  inclusive,  giving  the  phases  weights  i,  6,  4,  3,  2,  2,  2,  2: — 
Epoch  -  1 89,  JT  =  +  3  7'"  -  0.6  -/,  +  0.6  X  =  -}-  36"'  ±  O'". 


44  RESEARCHES  ON  THE  MOTtON  OF  TIIE.MOON. 

From  (17)  to  19),  giving  the  weights  3,   2,  2: — 

Epocli  +  134,  ^Tir  +  30'"  ±  S"". 

If  we  reduce  these  results  to  minutes  of  arc,  we  find  tlie  following  corrot^tions  to 
the  moon's  moan  lottgitudo,  as  derived  from  Hansen's  Tables : — 


Epoch. 

—  687 
-381 

—  189 

+  134 


ft. 


Wt. 

3 
2 


-ii'±4' 

-27' ±5' 

-  20'  ±3'  4 

-i6'±4'  3 

In  the  light  of  these  comparisons  with  theory,  wo  could  no  doubt  amend  some  of 
our  interpretations  of  the  times  given  by  Ptolemy.  I'tolemy's  interpretation  of  the 
description  of  the  first  ecV.pse  would  seem  to  be  more  correct  than  the  one  adopted, 
while,  in  the  case  of  eclipse  (9),  it  was  an  error  to  suppose  that  much  more  than  an  hour 
had  passed.  But,  although,  by  thus  amending  the  interin-etations,  a  better  agreement 
would  be  attained  among  the  observations,  I  do  not  think  the  final  result  wouhl  be 
improved,  and  it  certaiidy  would  not  be  materially  altered.  I  think  we  may  conclude, 
with  a  high  degree  of  probability,  that  during  the  eight  centuries  jn-eceding  the 
Christian  era  the  moan  longitude  of  the  moon  in  Hansen's  Tables  reipiires  a  correction 
of  about +  18'.* 

^  5- 

ARABIAN  OBSERVATIONS  OP   ECLIPSES,  EXTRACTED   FROM   CAUSSIN'S  TRANS- 
LATION OF  EBN  JOUNIS. 

Tlie  complete  French  title  of  this  work  is,  "Le  Livrc  lU  la  grnmh  Table  Ilah'mitc 
ohsrrire  jmr  le  Sheikh,  VImam,  le  docte,  le  savant  Ahoulha.smn  AH  ehn  Ahderrahman,  elm 
Ahmed,  ehn  Jounis,  ebn  Ahdalnala,  ehn  Mousa,  ehn  Mn'isara,  ehn.  Ilafes,  ehn  JIhjan. 
Traduif  par  le  C'"  Oaussin,  professeiir  de  la  lam/ue.  Arahe  an  College  de  France.  A  I'aris, 
de  I'imprimerie  do  la  Republiqiie.     An  xii.  [1804,  v.  s.]." 

Most  of  the  observations  wliich  will  be  quoted  were  also  published,  before  the 
appearance  of  the  book,  in  tho  IVIemoirs  of  the  I'aris  Academy  of  Sciences,  vol.  2; 
and  tliere  are  a  few  discrepancies  between  the  results  there  given  and  those  in  the 
extended  work.     I  shall,  however,  use  tho  latter  as  my  authority. 

The  ideas  of  the  author  respecting  the  errors  of  instruments  seem  to  have  been 
far  ahead  of  his  age,  if  we  may  judge  from  the  following  description  of  the  precautions 
which  must  be  taken  to  obtain  good  observations.  Unfortunately,  only  a  fraction  of 
the  observations  could  have  been  made  by  this  most  tiritical  observer,  who  died  in 
1008. 

"/>e  VErreiir  des  Instrumcns  qui  servent  a  mesurer. 

"Jj'art  ne  pouvant  atteindre,  dans  la  fabrication  des  instrumens,  la  justesse  qui 
con<,M>it  I'esprit  do  I'artiste,  soit  pour  egaliser  leur  surfaces,  soit  pour  les  divisor  et 

•Since  reai'tiing  this  conclusion,  I  have  been  strongly  inclined  to  think  that  the  phases  recordcil  should  be  con- 
sidered KS(<eonietriral  contacts,  and  therefore  that  Ai  and  Aj  should  bolh  be  regarded  as  zero.  This  change  would  make 
the  results  slighlly  more  consistent,  and  would  increase  the  tabular  correction  from  the  lirsl  group  of  observations.  I 
I  u.e  not,  however,  considered  it  advisable  to  introduce  it. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  45 

lea  centrer  sivec  iirc'cision,  il  faut  necessairemeiit  qu'ils  soient  sujets  i\  ties  erreurs 
provenant  do  quelqu'une  de  ces  causes  on  de  leur  situation  par  rapport  t\  I'liorizon. 
S'il  y  a  une  constnictirp  elle  est  sujet  h  des  devers  ou  apparens  ou  insensibles;  si  les 
instrumens  sent  de  bois,  le  bois  se  gauchit,  sur-tout  s'il  est  fixd  dans  un  lieu  expose  an 
soleil  et  j\l'humid'*^<i.  II  y  aura  toujours  d'autant  moins  d'erreurs  dans  lea  instrumens, 
qu'ils  auront  e(  nstruits  par  un  homuie  plus  instruit,  plus  habile  et  plus  attentif. 
A  ce  que  je  vi.  is  de  dire,  il  faut  ajouter,  dans  I'observateur,  I'habitudo  d'observer,  do 
placer  d'aploinb,  la  justesse  do  I'aplomb  lui-meme,  &c.  S'iniaginer  quo  clmcun  est  en 
(?tat  de  prendre  toute  esj)cco  de  mesuro  sans  en  avoir  I'habitude,  et  que  tons  los  instjni- 
mens  donnont  des  rt'sultats  silrs,  c'est  <^tre  dans  Torreur.  Celui  qui  veut  fairo  de 
bonnes  observations,  doit  s'appliquer  long-temps  i\  connoitre  les  instrumens  et  s'ac- 
coutumer  j\  s'en  servir." 

The  geographical  position  of  liagdad  does  not  seem  to  be  very  well  determined, 
but  the  observations  with  which  we  have  to  deal  are  so  rough  that  the  probable  error 
is  not  of  importance  in  the  present  investigation.  The  latest  determinations  I  can  find 
are  in  the  Connaissancc  des  Temps  for  1836,  Additions,  p.  138,  where  the  latitude, 
33°  19'  50",  is  tJiken  from  a  paper  by  liEAUCHAMP  in  Zach's  MonatUehe  Concspondem, 
^'ol.  i,  and  the  longitude  is  taken  from  a  note  to  the  same  })Hper.  The  following 
aj)pear  to  be  the  I'esults  of  the  separjito  determinations: — 

Conn,  des  Temps  for  1788     .     .     .  A  =  2''  48™  i8»  Som-co  unknown.            " '_ 

Ukauchamp,  Man.  Corr.,  vol.  i,  p.  65  2''  48"'  9"  Eclipse  Jup.  III.  Sat.       '  ^^^ 

Ukauciiamp,  Mon.  Corr.,  vol.  i,  p.  65  2''  47'"  38'  Eclipse  Jup.  I.  Sat.              % 

TiUESNECKER,Mo«.  CVr.,vol.  i,p.65  2''  48"  9'  Eclipse  O,  June  3,  1 788. 

These  longitudes  are  counted  from  Paris.     I  have  adopted  the  last  result,  which  is 
that  employed  in  the. recent  volumes  of  tlio  Connaissancc  des  Temps,  assuming 

Latitude  of  Bagdad 33°  20'  .   . 

Longitude  east  of  Greenwich 2''  57'"  30". 

The  longitude  may  be  considered  as  subject  to  a  probable  en-or  of  ten  or  fifteen  sec- 
onds, which  is  not  of  importance  at  jn-esent. 

The  position  of  Cairo  is  also  taken  from  recent  numbers  of  the  Connaissancc 
des  Temps,  as  follows: — 

Latitude 3°°  2' 

Longitude  from  Paris 1"  55"^  41"; 

whence, 

Longitude  from  Greenwich 2''     5"*     2". 

We  shall  first  copy  the  descriptions  of  the  observations  from  the  woi-k  in  ques- 
tion, and  then  present  the  results  in  a  tabular  form  as  far  as  possible.  I'^dipses  in 
which  the  data  are  entirely  insufficient  will  be  passed  over  in  silence. 

(i)  Page  84. — "Eclipse  de  soleil  ohserree  a  Bagdad  le  30  [29]  novemhre  829. 
Hauteur  du  soleil  au  commencement,  selon  lo  rapport  des  astrononu's,  7";  hauteur  i\ 
la  fin,  24°,  sur  les  trois  heures  du  jour  environ."  .  » 


46  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

The  local  mean  times  hence  deduced  are: — 

.  Beginning ig^  ^^"^  44- 

End 21''  24™  24". 

(2)  Page  88. — '^I'ldipsc  th  June  ohscrree  n  Bagdad  k  12  [11]  aoAt  854.  On 
observa  an  connnencoment  de  IVclipso,  la  hauteur  d'Aldel)arau  de  45°  30'  i\  I'orient: 
on  n'obscrva  point  d'autro  instant  ni  d'autro  circonstance  do  cetto  eclipse  que  I'instant 
du  eonuuencement,  qui  est  exact  et  precis." 

Result:  Local  mean  time  of  beginning 14''  58"  2)7*- 

(3)  Page  90. — "J5cli2)sc  do  lime  observrc  a  Bagdad  le  22  [21]  juin  856.  On 
observa  an  eonuuencement  de  I'e'clipse  la  hauteiu-  d'Aldebarau  de  9°  30'  i\  roriont." 

Result:  Local  mean  time  of  beginning 15''   19™  28*. 

(4)  Page  1 12. — "E'cUpse  do  huic  ohservcc  a  Bagundlc  i  juin  923.  *  *  la  fin  j\ 
3'',  henres  egalos ;  hauteur  de  IV'toile  jn-cs  de  la  <iueuo  du  Cygne  [«  ( 'ygni],  29°  30' 
j\  Torieut." 

Result :  Mean  time  of  end '  .     .     9''  54™     3". 

(5)  Page  114.— "J^JdijJSC  de  soldi  observ6c  a  Bagdad  le  11  [10]  novemhre  923. 
Nous  nous  reunimes  plusiours  pour  I'observer  et  uous  distinguruncs  clairement  ses 
circonstances.  Hauteur  du  soleil  au  milieu  de  I'eclipse  di'tcrmint'e  d'aprcs  I'estime  de 
tons  les  observateurs,  8°  orient;  la  fin  h  2''  12'",  henres  int'gales;  la  hauteur  alors 
de  20°." 

Result:  Local  me.an  time  of  middle 19''  19™  38' 

Local  mean  time  of  end 20''  30™     2". 

Of  course,  the  first  observation  can  have  no  astronomical  value. 

(6)  Page  1 16. — ^^]£dipsc  de  lime  ohservcc  a  Bagdad  le  1 1  avril  925.  J'ai  observai 
cette  c'clipse  et  j'ai  trouv(j  au  commencement  la  hauteur  d'Arctxu-us  de  11°  i\  I'orient ; 
hauteur  de  I'utoile  Wega,  }\  la  fin,  24°,  Le  commencement,  d'aprf-s  cette  observation, 
aiTiva  k  55',  henres  int'gales,  de  la  unit;  *  *  la  fin,  selon  I'observation,  4''  36'", 
henres  int'gales." 

Result :  Mean  time  of  beginning 5''  36™     6" 

Mean  time  of  eiul lo*"  45"  19'. 

There  is  clearly  an  en-or  in  the  statement  that  the  altitude  of  Arcturus  was  1 1  ° 
at  the  beginning  of  the  eclipse;  it  must  have  been  30°  or  upward.  I  cannot  see 
th.'it  any  other  bright  star  could  have  had  an  altitude  of  1 1  °  at  the  time  in  question, 
while  Arcturus  was  far  the  most  prominent  star  in  the  east.  It,  therefore,  seems  prob- 
able that  the  altitude  is  incorrectly  given.  We  shall,  therefore,  endeavor  to  deduce 
the  time  from  the  results  of  the  Arabian  calculations,  checking  the  latter  by  compari- 
son with  our  own.  The  sun  was  in  about  10°  north  declination  ;  the  geometricaP  set- 
ting of  his  centre,  therefore,  occurred  at  6''  26™  ajjparent  time,  or  6''  25"'  mean  time, 
and*each  temporary  hour  measured  about  5  5'".  7.     The  interval  given  by  the  Arabians 


RESEARCHES  ON  Tin;  MOTION  OF  THE  MOON.  47 

cuirespoiuls  to  4''  i6'".2  mean  tinio,  makhi}^  their  coiiiputod  tinio  of  oinliiij^-  10''  4i"'.2, 
Hliowiiif,^  an  error  of  four  inimites,  wliidi  would  1)0  diminiHlicd  if  wo  sujiposo  that  tliey 
apidied  seniidiameter  aud  refractiori  in  computing  the  time  of  sunHct.  (It  will  be 
noted  that  wo  hero  have  to  do  with  a  computed,  and  not  with  an  observed,  suiiHet.) 
Now,  for  tho  beginning  of  tho  eclipse,  55'  coireaponds  to  Si^.o  of  mean  time,  making 
their  computed  time  of  beginning  7''  i6"'.o.  Applying  tho  correction  of  4."'!,  wo 
have: — 

Probable  mean  time  of  beginning j""  20"*.  i. 

This  result  will  bo  8ubje4;t  to  an  error,  arising  from  the  error  in  tho  relative  positions 
of  Arcturus  and  a  Lyrre  adopted  by  tho  Arabians.  Tho  probable  amount  of  this  error 
will  not,  I  conceive,  exceed  two  or  three  minutes  of  time. 

(7)  Pago  118. — ^^ l'^cVi])se  lie  lune  ohscrvcc  a  Baythid  Ic  14  [13]  sejjfviiihe  c)2y.  Le 
connnencement  j\  10''  14™  do  la  nuit  do  vendredi,  lo  milieu  ii  11''  21",  la  fin  {\  9'"  du 
jour  do  vendredi,  lo  tout  en  heures  iiu'gales.  Get  eclipse,  dit-il,  fut  observc'e  par  mon 
ills  Aboulhassan.  Hauteur  do  Sirius  an  connnencement,  3 1  °  i\  I'orient ;  revolution  do 
la  sphere  depuis  lo  coucher  du  soleil  jusqu'au  commencement  do  IV'clipse,  determinc'e 
avec  I'astrohibo,  148°  environ." 

From  what  follows,  it  apjiears  that  tho  times  given  an;  those  computed  from  the 
tables.     From  the  altitude  of  Sirius  wo  have : — 

Local  mean  time  of  beginning .     .     15''  48'"  16". 

Tho  observation  with  the  astrolabe  gives  a  result  only  one  or  two  minutes  later. 

(8)  Pago  120. — "]'Jcli2)se  dc  soldi  ohscrvee  a  Bagdad  Ic  18  [17]  aoiit  928.  Lo 
soleil  80  leva  (^clipse  d'un  pou  moins  du  quart  do  sa  surface.  *  *  *  Nous  obser- 
vAmes  lo  soleil  dans  I'eau  d'une  manicre  sAre  ot  distincto.  Nous  trouvamos  i\  la  fin 
lorsqu'aucuno  partie  du  soleil  nV'toit  plus  (.'clipsc'e,  et  que  son  disque  paroissoit  entier 
dans  I'eau,  la  hauteur  de  12°  i\  I'orient,  moins  le  tiers  d'une  division  do  I'instrument 
divise  par  tiers  de  degr(5,  co  qui  fait  retrancher  I  do  degrt^.     (Hauteur,  1 1°  53'  20".)" 

Result:  Mean  time  of  end 18"  26"  59'. 

(9)  Pago  122. — ^'l^cUjise  de  bine  ohsertre  a  Ihujdad  le  2y  Janvier  929.  J'ai  ob- 
serv*^,  dit-il,  le  commencement  do  cetto  eclipse.  La  hauteur  d' Arcturus  ctoit  alors  18° 
k  I'orient." 

Result:  Local  mean  time  of  beginning 11''     3™     2". 

(10)  Page  124. — ^'£clipse  de  I inic  ohscrvee  ii  Bafjdud  le  5  [4]  noremhre  933.  J'ai 
observ(i,  dit-il,  cette  c'cHpso  lorsquo  la  lune  common^a  51  s'obscurcir.  La  hauteur  d'Arc- 
turus  etoit  alors  15°  i\  I'orient." 

Result.:  Local  mean  time .     .  "  .   '.     .     16''  15™  15". 

IMie  remaining  oclipsoF  were  observed  at  Cairo. 

(11)  Page  164. — ^^£cripse  de  soleil  ohservee  nu  Caire  le  12  dcccmhre  977.  Cliacun 
attendoit  le  comraenccinent  de  I't'clipse ;  elle  parut  sensible  a  la  vue  lorsque  la  hauteur 


^8  RKSKARfllKS  ON  Tin;  MOIION  (»!■  Tin:  MOON. 

«hi  Holoil  I'toit  I'lili'o  15  et  16  dcf^ivH.  *  «  *  |,„  soloil  piinit  icpntmlrt)  todto  sa 
(•lark';  i)t  jo  truiiva  sa  hauteur  ^^"^  20'  environ,  cliacun  t'tant  d'accunl  do  la  lin  do 
I't'clipso." 

Jjosidt :  The  ochpso  Honsible  to  the  view     ......     20''  24'"    4* 

No  longer  visildo 22'' 41"  12". 

(12)  I'ago  166. — "J'\Uj)se  ih:  soldi  okscrvce  an  Caire  le  8  Jiiin  q-S.  Ilantonr  dn 
Holeil,  lors(iuo  rc'clipse  conmien(;a  fi  etro  sensible  aux  youx,  56"  environ ;  hauteui'  i'l  la 
tin,  26'  environ."  .* 

Result:  The  eclipse  sensible  to  the  view ^ii  j^"' ^j* 

The  eclipse  ended V' 47'"  '5"- 

(13)  Pago  168. — "Jv'(?/j«(!  de  htm;  obscrree  an  Cdiic  Ic  14  iixii  979.  lia  (in  d(i 
I'c'clip.'^e  h  une  houro  1 2'  do  la  unit,  heures  I'gales." 

IFere  wo  have  to  accept  the  results  of  the  Arabian  astronomer  without  any  ot"  the 
data  by  which  he  determined  his  time.*  "^^I'he  geometrical  setting «»!'  the  sun's  centre  was 
at  6''  49'"  ajjparent  time,  and  6''  43""  mean  time  It'  we  allow  2  minutes  for  refraction, 
it  will  make  the  mean  time  of  counnencement  7''  57'",  a  result  which  is  uncertain  by 
several  minutes. 

(14)  Page  168. — ^^  J'Jilipse  lie  soldi  ohscrrcc  an  Cuhe  le  28  iiKii  <.)yg.  Hauteur  du 
soluil  lorsque  reclipae  fut  sensible  h  ia  vuo,  6"  30'.     Lo  soleil  so  concha  eclipse." 

Result:  The  eclipse  sensible  to  the  sight 6''  18'"    o". 

( 1 5)  I'age  1 68 — "Eclipse  de  lane  obserrec  au  Caire  le  7  [6]  iiovembre  979.  Hauteur 
au  comniencoment„  64"  30'  orient;  hauteiu*  i\  la  fin,  65°  Occident,  environ." 

Result,  supposing  the  altitudes  to  bo  those  of  the  moon,  which  is  not  distinctly 
stated : — 

lieginning       10''    9'"  50" 

End 13"  22"  46". 

( 1 6)  Page  1 70. — " j''"t'?(/we  totale  de  lune  observee  au  Caire  le  3  [2]  mai  9S0.  Hauteur 
de  la  lune  au  commencement,  47°  40' ;  la  fin,  36'  environ,  heures  t'gales,  avant  la  fin 
do  la  nuit." 

This  altitude  of  the  moon  assigned  by  the  observation  exceeds  the  actual  meridian 
altitude,  so  that  there  is  some  mistake  which  prevents  the  beginning  being  used.  For 
the  end  we  have : — 

Apparent  time  of  sunrise,  ©'s  declination  being  ij'^.o     .  17''  i9"'.4 

The  interval  as  given  by  the  Arabs —       36'".o 

Equation  of  time —          5"'.3 

Longitude —  2''    s^.o 

Greenwich  mean  time  of  ending       14'*  33"°.  i. 

*  After  completing  the  discussion  of  these  eclipses,  I  am  inclined  to  suspect  that  this  may  lie  a  calculated  and  not  an 
observed  time.  As  the  result  would  not  be  appreciably  altered  by  the  suppression  of  the  observation,  I  have  let  the  eclipse 
remain. 


RKSEARCHES  ON  THE  MOTION  OF  THE  MOON.  49 

( 1 7)  l'n}^i)  1 70. — "  £cli}).sc  (le  lime  obscrvce  au  Caire  /'!  2  3  [21]  nvril  98 1 .  I  laiittjiir 
(le  la  lune  an  comruencement,  21°  environ;  grandenr,  lo  qnart  dn  diiinietro  onvinui ; 
fin  de  I't'clipHe,  un  quart  d'heure  environ  avant  le  lever  dn  H(tleil." 

Local  mean  time  of  beginning 15''  2H'"     38" 

For  the  end  we  have  app.  time  of  sunrise  (Dec.  zr+  i3°.8)   17''  2  7"'.4 

Interval  as  given       —        15™ 

Equation  of  time       ...«..•       "~         3'"  7 

Longitude —2''    5"'.o 

Greenwich  mean  time  of  end 15''    3"'.7. 

(18)  Page  170. — ^^ Eclipse  de  lune  ohnervee  au  ('aire  le  15  octohrc  981.  Grandeur 
de  Wclipse,  5  doigts  environ  du  diami^tre ;  hauteur  de  la  lune  lors  de  rattouclnnent 
par  dehors,  selon  mon  dvaluation,  24°." 

Local  mean  time  of  beginning       .     .     # 16''  18"'  15". 

(19)  Pago  172. — ^^ /Jclipse  totale  de  lune  observee  au  Caire  le  1  mars  gS^.  Hauteur 
de  la  lune  lorsque  I'tkdipse  parut  sensible,  66°  ;  hauteur  lorsque  la  lune  eut  repris  sa 
clarte,  35°  50' ;  durde  de  I't^clipse  totale  une  heure,  environ  " 

Here,  again,  the  first  altitude  assigned  is  impossible.  From  the  second  we  de- 
duce:— 

Local  mean  time  of  ending 15'' 38'"    o". 

(20)  Page  172 — '^  Eclipse  dc  soleil  observee  au  Caire  le  20  juillet  985.  Hauteur 
du  soleil  au  commencement  de  I'c^clipse,  23°  environ  ;  hauteur  a  la  fin,  lorscpie  IV'dipso 
n'dtoit  plus  sensible  Jl  Ifi  vue,  6° ;  grandeur  de  I't^clipse,  un  quart  du  diam^tre." 

Local  mean  time  of  beginning 5''     i"  32" 

Local  mean  time  of  end 6'' 23™  15'. 

(21)  Page  172. — "  ^Eclipse  de  lune  observee  au  Caire  le  19  [18]  decembre  986. 
Hauteur  de  la  lune  au  commencement  de  I'eclipse  visible,  24°  Occident.  J'ai  evalue  la 
hauteur  au  moment  de  I'attouchement,  50°  30' ;  grandeur,  10  doigts  du  diametre.  La 
lune  se  coucha  ^clips^e." 

I  can  give  no  explanation  of  this  second  observation.     From  the  first  altitude  we 

have  :— 

Local  mean  time  of  commencement 16'' 56™    4'. 

(22)  Page  174. — ''Eclipse  de  lune  observee  au  Caire  le  12  avril  990.  Hauteur  de 
la  lune,  au  commencement,  je  veux  dire,  au  moment  de  I'attouchement,  38°." 

Local  mean  time  of  "attouchement"       Q*"  45""  59"- 

(23)  Page  1 74 — "  ilelipse  de  soleil  observee  au  Caire  le  20  [  19]  aout  993.  Hauteur 
du  soleil,  au  commencement  de  I'eclipse,  27°  orient;  hauteur  au  moment  de  la  plus 
grande  phase,  45°  orient;  hauteur  k  la  fin,  60°  orient;  grandeur,  §  de  la  surface." 

Result:  Mean  time  of  commencement 19"  41""  23' 

Mean  time  of  the  end 22"  22""  37'. 

7 75AP.  2 


JO  RESEARCHES  0\  THE  MOTION  OF  THE  MOON. 

(24)  Pajfo  176. — ^^  P^dipfif  totalc  lie  liim  observre  an  Cairr,  le  i  mats  1002.  LVclipno 
flit  totalo  avtsc  donieuro  duns  r(>iiil)ris.  llautuur  d'ArcturuH  au  coiniiu'iicuiiient,  52° 
orient;  liauteiir  do  IVtoilo  a  du  coclier,  14"  Occident;  Inuiteiir  d'Arcturus  i\  la  fin,  35°." 

On  tlicHe  inconHJHtt'nt  altitndes  of  ArctnruH,  Cath.sin  remarks  that  the  altitude  at 
coniniciicenicnt  may  l>o  either  12°  or  52°,  but  Houvakd  advised  him  that  the  latter 
readinjf  nuist  he  taken.  The  last  altitude  of  Arcturus,  35°,  admits  of  no  doubt  in  read- 
ing. The  star  which  had  the  altitude  14°  is  also  doubtful,  the  name  given  in  the 
niaMuscript  not  l»eing  found  in  the  Arabian  Htar  Catalogues;  but  he  found  a  similar 
name  in  ScAi.KiK.K  as  j)ertaining  to  a  Aurig.'c. 
The  results  for  begiiming  are  : — 

Fnmi  altitude  of  Arcturus 11'' 41"  23*^ 

Krom  altitu(hM)f  a  AurigiP 11'' 45"' 40' 

Adoj)ted  rf'sult ii''43'"    2'. 

(25)  l*ago  178 — "  £V7/y),w  (h  soldi  ohservre  an  Cairs  h  24  [23]  Janvier  1004. 
(Jrandeur  d((  I'cclipse,  11  doigts  ;  hauteur  du  soleil,  lorso^ue  I'dclipse  commen(,'a  a  pa- 
roitre  sur  son  dis(pu',  16°  30'  Occident;  connnencement  e.stim<5  h  18°  30';  hauteur 
lorsque  le  (puirt  du  diam^tre  f^toit  t'clipsd,  15°;  hauteur  lorsque  la  nioitid  du  dian:&tre 
fut  edipsi'o,  10°  ;  hauteur  au  moment  de  la  plus  grande  phase,  5°." 

The  diti'erence  of  the  first  two  altitudes  is  surprising,  corresponding  as  it  does  to 
1 1  minutes  of  time.     The  results  are  : — 

The  eclipse  sensible 4''    6"  13* 

Estimated  time  of  beginning ...      3'' 55"°  17*. 

The  local  mean  times  have  been  reduced  to  Greenwich 'mean  time  by  applying 
the  longitudes  already  given,  and  the  results  are  shown  in  tabular  form  in  the  follow- 
ing pages.  The  tabular  geocentric  positions  of  tie  moon  are  fii-st  given,  the  times  of 
computjition  being  generally  nearly  the  same  with  those  of  observation.  In  comput- 
ing the  longitudes,  the  double-entry  tables  have  been  omitted  and  tlie  constant  22240 
added,  a  proceeding  which  involves  a  mean  error  of  ±  14"  in  the  longitudes.  The 
moon's  motion  in  latitude  is  omitted ;  it  will  be  sufficient  to  suppose  it  equal  to  i  the 
motion  in  longitude.  Its  algebraic  sign  is,  however,  given  immediately  after  the  lati- 
tude itself. 

Respecting  the  places  of  the  sun,  it  is  only  necessary  to  say  that  they  are  from 
Hansen's  Tables, 


kr:sEAR(MjEs  on  the  motion  of  the  moon, 

Tabular  Pcsitions  of  the  Moon  and  the  Sun  /or  the  Aralnan  Obsenuilions, 


5' 


No.  of 

C5r.  M.  T.      Moon's 

Mot.  in 

.'•'0 
Latitude  ; 

Paral- 

The  Sun's 

T 

Log.  of 
Radius 
vector. 

I 

1 

Semi- 

Eclipse. 

Dato  and  Phce. 

of  Coin-    Longitude 

0''.OI. 

increasing  +- 

lax. 

^ongilude. 

diam. 

pulalion. 

diininislilng- 

1 

i 

B.lgiitld. 

h    m     t\ 

•          t 

• 

f 

•           1 

i 

t 

83ij,iNov.   39 

16  36  14 

251   37.6 

7.86 

+   22,1    - 

56.9 

353     37.0 

9.99270 

16.2 

18  36  54 

252  38.1 

7.87 

H-    16.8    - 

56.9 

353     41-7 

9.99269 

16.2 

J     a 

85.(,  Aug.   II 

13     I     7 

321  403 

8.81 

+     18.3    + 

60,3 

143     35.4 

15-9 

J     3 

836,  June   31 

13  21  58 

373  34.5 

8.25 

-  45-2    + 

58.1 

94     10.  fi 

.     .     . 

I5-7 

D     4 

933,  Juno     I 

fi  56  33 

255  '9.8 

8.60 

-  43-8   - 

59.6 

74     43-4 

.     .     . 

15.8 

S 

023,  Nov.   10 

16  21     8      232  37.3 

9.07 

4-   33.4   - 

(.1.3 

233     26.8 

999355 

Ifi,3 

17  32  32      333  22.4 

9.07 

+    28.2   - 

bl.2 

233     29.8 

9-99354     '' 

16. a 

J)     6 

935,  April  11 

2  38  36      204  16.7 

8.43 

+   3&-8  - 

59  0 

26       8.0 

.     .     . 

'5-9 

7  •17  49 

207  18.5 

8.46 

+20.1    — 

59-1 

26     20.5 

•     • 

15.9 

J     7 

937,  Sept.   13 

12  50  46 

354  28.7 

9.09 

+    5''2    + 

61.3 

175      '2.0 

.     .      . 

1(1.0 

8 

938,  Aug.   17 

15  29  29 

149     7-5 

7.8fi 

-    13.1    - 

56.9 

149     37-0 

0.00304 

15.9 

3)     9 

929.  Jan.     37 

8    5  3» 

131  48.5 

8.51 

+  30.6    - 

59.3 

3'3     '4.1 

.     .     , 

16.3 

]>    10 

933,  Nov.     4 
Cairo. 

•3  «7   15 

46  54-7 

7.24 

-     5.9  - 

54-5 

227     48.8 

1O.3 

II 

977,  Dec.    12 

18  19    3 

365  49.0 

9. II 

+  35-2  - 

61.4 

367       1.7 

9.99106 

J6.3 

30  36    10 

267  16. I 

9.11 

+   27.3  - 

61.4 

367       7-5 

9.99105 

16.3 

13 

978,  June     8 

0  32   29 

i     81   58.5 

7.10 

-      0.2    f 

54.0 

81  ■  48.9 

0.00733 

'5.7 

• 
2  42    13 

\     83     7.3 

7.10 

+     0.3  + 

54.0 

81     54.4 

0,00735 

15-7 

J    13 

979,  May     14 

?  52    0     238  51.2 

8.30 

+   32-5  - 

58.5 

57     57.0 

•      •      • 

15.8 

M 

979,  May    28 

4  12  58  ,     71  475 

7.61 

+   39-0   + 

55-9 

71      '5.' 

0.00713 

13.8 

3)   15 

979,  Nov.     6 

8     3  40  1     48  42-7 

8.31 

--   37-6  + 

58.6 

229     27.1 

•      •      • 

16.3 

II   18     0  i     50  34.8 

8.29 

—  27.2  + 

58.5 

229     35-3 

•      •      • 

16.2 

J)    I6 

980,  May      2 

14  26    0  1  328  24.4 

7-47 

—    12.0  — 

55-4 

47     31-3 

■      •      ■ 

15.8 

J    "7 

981,  April  31 

13  28     0  i  216  14.9 

7.09 

-  45-9  - 

53-9 

36     46.0 

'5.9 

I   18, 

981,  Oct.     15 

14     7     0       27  24.4 

9-03 

4-  46.6  + 

61. 1 

208       1.6 

•     •      • 

i  16. 1 

J)    19 

983,  Mar.      I 

9  55     0  ,   165   18.7 

8.64 

+   31.9  - 

59.7 

346     '3.3 

16. 1 

13  40    0      167  33.5 

8.61 

+    19-4   - 

59.6 

34O     22.6 

.      .      . 

i  16. 1 

20 

985,  July     20 

2  56  30      122  43  3 

8.17 

+    150  ~ 

58.0 

122     17.6 

0,00587 

,15.8 

4  18  13      123  29.7 

8.18 

+    10.9  — 

58.1 

122     20.9 

0.00587 

1  15.8 

1 

])    21 

986,  Dec.    18 

"4  53     0  i     92  '^•9 

7.10 

+    3"-3  - 

54.0 

272     49-4 

'6-3 

])    33 

990,  April  12 

7  42    0  1  306  43.9 

7.10 

-  37-5  + 

54.0 

27     34-2 

•     •      • 

15.9 

II    4    0  ;  208  23.4 

7.IO 

—  28. 3  4- 

53-9 

27     42.4 

.     .      . 

13.9 

33 

993,  Aug.   19 

17  36     5      150  28.6 

9-04 

4-      5-3  + 

&I.I 

151     54-6 

0  00288 

15.9 

S    24 

1002,  Mar,     I 

9  41   18      165  37-4 

9-13 

—    12. I   — 

61.4 

346     3&.0 

• 

16. 1 

25 

1004,  Jan.    34 

I   51     0  1  310    9.4 

8-39 

-t-    15-8  4- 

58.8 

308     43-3 

9-99444 

1(1.3 

52 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Comparison  of  Tabular  and  Observed  Times  for  the  Arabian  Observations. 


o.  of 
Eclipse. 


Dale  and  Place 


2 

3 
4 

•5 
6 


9 

10 


>3 
14 
15 

l6 

«7 

I8 

>0 


829,  Nov.  29 

854,  Aug.  1 1 
856,  )une2i 
g23,June  i 
923,  Nov,  10 
925,  Apr.  II 

o/iT.  Sept.  13 

928,  Aug.  17 

929,  Jan.  27 
933,  Nov.   4 

Cairo. 

977,  Dec.  12 

978,  June   8 

979,  May  14 
979,  May  28 

979,  Nov.   6 

980,  May     2 

981,  Apr.  21 

981,  Oct.  15 
983,  Mar.    I 

.,35,  July  20 


24 


21 

986,  Dec.  18 

22 

990,  Apr.  12 

23 

993,  Aug.  19 

Phenomenon 
Observed. 


1002,  Mar.    I 


25       1004,  Jan.  34 


0  Keginnlng 
0  Ending 
J)    Beginning 
2)    Beginning 
})   Ending 
0  Ending 
J)    Beginning 
])    Ending 
})    Beginning 
0  Ending 
])   Beginning 
])   Beginning 


0  Beginning  (S.) 

0  Ending 

0  Beginning  (S 

Q  Ending 

])   Ending 

0  Beginning  (S, 

})   Beginning 

D    Ending 

D    Beginning 

])   Ending 

D   Beginning 

J>   Ending 

D    Beginning 

])    Beginning  (S, 

})   Ending 

0  Beginning 

0  Ending 

3)   Beginning  (S.) 

3>    Beginning  (at) 

0   Beginning 

0  Ending 

)   Beginning 

D   Endiiig 

0  Beginning  (est. 


Local  M.  T. 
Obs. 


"9  33  44 

21  24  24 

"4  58  37 

15  iq  28 

9  54  3 

20  30  2 

7  20  6 

10  45  19 

15  48  16 
18  26  59 
1132 

16  15  15 


20 

22 

2 

4 

7 

6 

10 

■3 

16 
15 
'7 
16 

15 

5 

6 

16 

9 

>') 

22 

II 


24  4 

41  12 

27  31 

47  15 

57  2 

18  o 

.9  50 

22  52 

38  8 

28  42 
8  44 

18  15 

37  58 

I  32 

23  "5 
56  6 

45  59 

41  23 

22  37 

43  a 


3     55     >7 


Gr. 

M.  T.  of 

Obs. 

h 

m      s 

l6 

36  14 

18 

26  54 

12 

'   7 

12 

21  58 

6 

56  33 

17 

32  32 

4 

22   36: 

7 

47  49 

12 

50  46 

«5 

29  29 

8 

5  32 

:3 

17  45 

18 

ig   2 

20 

36  10 

0 

22   29 

2 

42   13 

5 

52   0. 

4 

12   58 

3 

4   48 

II 

17   50 

D 

too  high 

14 

33  06 

»3 

23  40 

15 

3  42 

14 

13  13 

loo  high 

■3 

32  56 

2 

56  30 

4 

18  13 

14 

5«   4 

7 

40  57 

17 

36   21 

20 

"7  35 

9 

38   0 

unavailable  | 

I 

50  15 

Tabul 

a 

Gr.  Time  of 

Geomet. 

Phase. 

h     m 

5 

15  50 

20 

18   8 

56 

II  53 

59 

T2   18 

13 

6  49 

49 

17  15 

50 

4  27 

8 

7  45 

35 

13   4 

I 

15  19 

26 

9   4 

20 

13  15 

54 

18  10 

30 

20  33 

0 

23  57 

47 

2  38 

20 

5  40 

44 

4   2 

38 

8   I 

26 

II   3 

55 

10  39 

0 

14  28 

19 

13  20 

50 

15   5 

l3 

13  58 

25 

9  59 

39 

13  15 

14 

2  3a 

10 

4   3 

32 

14  28 

56 

3   6 

9 

17  36 

I 

19  57 

43 

9  35 

28 

12  59 

2 

I  39 

6 

A.' 


H-  45. 

+  18. 

+  7. 

+  3. 

+  6, 

+  16. 

-  4. 
+  », 

-  13 


+ 

10. 0 

- 

58.8 

+ 

1.8 

+ 

3.5 

+ 

3-2 

+ 

24.7 

+ 

3.5 

+ 

II. 3 

+ 

10.2 

+ 

3-4 

+ 

13.9 

+ 

4- 

+ 

2.8 

- 

1.6 

+ 

14.8 

+ 

17-7 

+ 

24.3 

+ 

14-7 

+ 

22.1 

- 

25.2 

+ 

0.3 

+ 

19.9 

+ 

2.5 

+ 

II. I 

0.51 

0.42 

0.51 


0.40 

0.51 


0.45 
0.51 


0.37 
0.35 
0.28 
0.48 
0.51 

0.52 

0.51 


0.43 

0.62 

0.51 

0.41 

0.51 


0.44 


A/ 


Cla*s. 


-  23-2 

-  7.6 

-  3-6 

-  I  9 

-  3-4 

-  6.7 
■f  2-3 

-  1. 1 
+  6.7 

-  4.5 
+  29-7 

-  0.9 


-  3-2 

-  I.I 

-  6.9 
+  1.9 

-  5.8 

-  5-3 

-  1-7 

-  70 

-  2.4 

-  14 

4-  U.8 

-  7.7 

-  •B,  ^ 

-  10.6 

-  91 

-  II. a 

+  12.8 

-  0.1 

-  10.2  I 

-  1.3  I 

-  4.4  I 


Researches  on  the  motion  of  the  moon. 


53 


Next  is  8hf>wn  the  comparison  of  the  tabular  and  observed  times.  In  the  cohimn 
"  Phenomenon  «  bserved  ",  S.  signifies  that  the  time  of  observation  is  that  at  which  the 
echpse  was  said  i'^  be  sensible  to  the  sight,  whereas,  in  other  cases,  only  the  phrase 
beginning  or  ending  is  used.  As  these  phenomena  necessarily  occur  after  the  times 
of  geometric  fii-st  contact,  they  must  be  a  little  too  late.  The  observed  times  of  ending 
must  be  supposed  too  early  by  a  less  amount.  In  the  table,  however,  the  comparisons 
are  made  with  the  geometric  contacts  only.  Column  Jt  shows  the  difference  between 
the  observed  time  and  the  computed  tabular  time  of  the  geometric  phase.  It  is  next 
necessary  to  multiply  this  difference  by  the  appropriate  factor  to  reduce  it  to  correction 
of  the  moon's  mean  longitude.     For  the  required  factor  has  been  taken 

dt        de' 

these  quantities  being  computed  by  the  formula;  given  in  the  next  section,  on  the 
reduction  of  eclipses  and  occultations.  In  the  case  of  eclipses  of  the  moon,  the 
factor  may  be  supposed  to  have  the  constant  value  0.51.  Column  Jl  gives  the  indi- 
vidual corrections  to  the  moon's  mean  longitude  thus  obtained. 

In  the  last  column,  an  attempt  is  made  to  classify  the  results.  The  letter  a  gener- 
ally signifies  that  the  materials  for  the  determination  of  time  are  unexceptionable ;  b, 
that  there  is  room  for  error,  owing  to  the  vertical  circle  drawn  through  the  object  of 
which  the  altitude  w  as  observed  for  time  being  too  near  the  meridian,  or  to  the  eclipse 
being  a  smnil  one ;  c,  that  the  data  for  time  are  yet  more  defective,  or  that  the  time 
determined  by  the  observers  had  to  be  used. 

Passing  now  to  the  consideration  of  the  results,  we  remark  that  these  observations 
are  not  of  the  class  in  which  a  system  of  weights  determined  a  priori  can  be  adhered 
to,  owing  to  the  liability  of  the  observations  to  abnormal  errors.  With  a  view  of  form- 
ing a  judgment  how  far  the  observations  are  thus  affected,  we  begin  by  finding  the 
narrowest  limit?  within  which  a  majority  of  the  results  can  be  included,  making  no 
distinction  of  weights,  and  Including  all  discordant  observations.  We  readily  find 
these  limits  of  Jl  to  be  —  o'.8  and  —  6'. 8,  between  which  are  included  1 7  out  of 
the  33  results.  This,  taken  alone,  would  indicate  a  mean  correction  of  —  3'.8,  and  a 
probable  error  of  3'  for  each  observation.  Extending  the  limits  still  farther,  we  find 
that  27  out  of  the  ^^  are  contained  on  or  between  the  lii.ilts  +  2'. 3  and  —  10'. 6,  or, 
omitting  the  two  contained  on  these  limits,  three  fourths  of  the  whole  number  of  results 
are  contained  between  them,  while  the  outlying  results  are  eq:uil  in  number  on  each 
side.  This  would  indicate  an  individual  probable  error  of  3'. 8,  with  nearly  the  same 
mean  result. 

Reversing  the  reasoning,  if  we  suppose  a  probable  error  of  3',  then  three  fourths 
of  the  whole  number  of  observations,  or  25  in  all,  ought  to  be  contained  between 
limits  extending  through  10'. 2,  while  27  should  be  contained  between  limits  differing 
by  1 2',  and  the  remaining  6  should  lie  but  little  outside  the  limits,  always  supposing 
the  admitted  law  of  error  to  hold.  Most  of  the  six  outlying  observations  are  so  far 
from  fulfilling  this  condition  as  to  show  conclusively  that  the  law  in  question  does 
not  hold,  and,  therefore,  that  the  arithmetical  mean  is  not  the  most  probable  final  result. 


54 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


The  following  results  are  so  far  outside  the  limits  of  probable  error  as  to  be  sus- 
picious, if  not  certainly  abnormal : — 

829,  November  29. — Beg'mning. — The  tables  show  that  the  eclipse  began  at  or 
before  sunrise.  How  a  real  beginning  could  have  been  observed  more  than  half  an 
hour  afterward,  it  is  hard  to  see      The  observation  is,  therefore,  clearly  inadmissible. 

927,  September  13. — Though  the  time  from  the  altitude  of  Sirius  is  of  the  second 
order  of  accuracy,  the  observation  with  the  astrolabe  confirms  it,  so  that  the  discrep- 
ancy is  hard  to  account  for.  Possibly,  the  keen  eye  of  the  young  observer  caught  the 
penumbra  some  time  before  the  actual  advent  of  the  shadow.  The  smallness  of  the 
e-  '^36  would  only  admit  of  giving  half  weight  to  the  observation,  even  were  the 
resitJt  good. 

929,  January  27. — Nothing  can  be  done  with  this  eclipse,  the  observed  time 
appearing  exceptionably  free  from  a  liability  to  possible  eiTor. 

990,  April  12. — Here  we  have  nothing  to  check  the  record  that  the  moon  was  ^^i"^ 
high  "au  moment  de  I'attouchement ".  I  think  the  result  should  be  rejected,  espe- 
cially as  the  term  translated  attouchement  seems  to  be  of  doubtful  meaning. 

Of  the  four  discordatit  eclipses,  there  will,  I  conceive,  be  no  question  that  those  of 
829,  929,  and  990  should  be  rejected.  Respecting  that  of  927,  doubt  maybe  enter- 
tained ;  I,  therefore,  retain  it.  In  taking  the  mean,  it  may  seem  advisable  to  give 
classes  b  and  c  half  weight,  compared  with  a. 

We  have,  before  taking  any  means,  to  consider  the  cases  of  those  eclipses  of 
which  the  phases  of  beginning  are  distinctly  stated  to  be  those  when  the  eclipse  was 
apparent  to  the  view,  which  are  marked  (S.)  in  the  third  column.  It  might  seem  that 
all  the  observed  beginnings  should  be  referred  to  this  phase,  but  the  general  run  of 
the  comparisons  seems  to  favor  the  belief  that  the  times  were  made  to  refer  to  the 
actual  contacts  by  an  estimate  of  the  observer  in  each  case.  The  correction  to  be 
applied  for  the  phase  in  question  does  not  admit  of  a  definite  determination,  but  must 
rest  upon  our  estimate  of  the  acuteness  of  the  Arab  vision.  1  conceive  that  we  may 
assume  2  J',  a  probable  mean  correction  to  reduce  to  geometrical  contact;  but  what  we 
really  want  to  do  is,  not  to  reduce  to  real  contact,  but  to  the  greatest  phase  of  invisi- 
bility, so  that  the  times  of  beginnings  shall  correspond  to  those  of  the  endings  when 
the  eclipse  was  no  longer  visible  We  shall,  therefore,  apply  a  correction  of  plus  i'.5 
to  each  value  of  Jl  dependent  on  a  phase  of  beginning  marked  (S.).  The  observa- 
tions are  clearly  divisible  into  three  groups,  separated  by  pretty  wide  intervals.  The 
mean  results  are: — 

850         Jl  =  —  3'.8  ±  2'.4  3  phases. 

927  —  i'.6±i'.7  7  jihasea. 

986  —  4'.5  ±  I '.3         20  phases. 

The  probable  errors  are  obtained  on  the  supposition  tliat  the  probable  error  of  a 
result  of  class  b  is  ±4'. 5,  and  that  each  grouj)  is  affected  with  a  probable  systematic 
error  of  :i=  i'  in  addition  to  all  accidental  errors. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


$^ 


§6. 


MODE    OF    DEDUCING 


THE    EBROKS    OF    THE    LUNAK 
ECLIPSES  AND  OCCULTATIONS. 


ELEMENTS    FUOM    TUE 


The  method  of  computing  eclipses  and  occultations  may  generally  be  divided, 
though  not  perhaps  with  entire  sharpness,  into  two  classes:  in  the  one,  the  position  of 
the  observer  relatively  to  the  cone,  or  cylinder,  which  circumscribes  the  moon  and  the 
occulted  object  is  computed  by  geometric  methods,  and  the  condition  of  an  occulta- 
tion  or  of  the  beginning  or  end  of  an  eclipse  is  that  the  observer  shall  be  on  the 
surface  of  this  cone;  in  the  second  class,  the  apparent  position  and  magnitude  of  tlie 
two  bodies,  as  seen  by  the  observer,  are  computed,  and  the  corresponding  condition  is, 
.that  the  apparent  distance  of  centres  shall  be  equal  to  the  sum  of  the  apparent  semi- 
diameters.  The  first  method  is  preferable  on  the  score  of  elegance  of  treatment  and 
of  general  certainty  and  convenience  in  cases  where  the  phenomenon  has  been 
observed  from  several  stations.  It  requires,  however,  that  the  positions  of  both  bodies 
be  known  before  the  computations  of  the  phenomenon  are  commenced.  This  require- 
ment has  prevented  its  use  in  the  present  investigation,  because  it  was  desirable  to 
postpone  the  final  determination  of  the  positions  of  the  stars  to  the  latest  practicable 
moment,  in  order  that  the  best  available  data  might  be  used.  The  method  adopted  is, 
therefore,  to  determine  separately  and  independently  the  apparent  })08iti6ns  of  the 
moon  and  of  the  sun  or  star,  and  then  to  deduce  equations  of  condition  from  the 
difference  between  the  computed  distance  of  centres  and  the  sum  of  the  semi-diame- 
ters; or,  in  the  case  of  solar  eclipses,  from  the  differen<e  between  the  observed  and 
computed  phases. 

In  this  computation,  I  have  used  celestial  '  ngitndes  and  latitudes  throughout, 
and  not  right  ascensions  and  declinations.     ^^  there  is,  peiliaps,  no  difiereiice  in 

the  amount  of  labor  involved  in  the  two  methods,  tiic  method  inlnpttd  is  reconuminU'd 
by  the  greater  siniplicity  and  directness  of  the  computations,  the  ease  with  which  tliey 
can  be  controlled,  and  the  slightness  of  the  modification  wiinh  will  be  neces<ary  if  the 
results  desired  are  only  approximate.  These  advantages  are  ispetially  seiii  in  the 
computation  of  the  apparent  place  of  the  star,  which  is  so  much  more  simple  when  the 
longitude  and  latitude  are  required  than  in  the  case  of  the  right  ascension  and  declina- 
tion, that  when  two  or  three  places  are  required  for  distant' epochs,  the  labor  of  trans- 
fomiing  the  co-ordinates  of  the  star  may  be  fully  compensated  by  the  ctjiisequ'-nt  ease 
with  which  its  apparent  place  can  be  determined. 

The  investigation  of  the  formulae  actually  used  is  as  follows: — 


Put 


1. — Apparent  Place  of  the  Moon. 


r,  I,  b,    the  geocentric  radius- vector,  longitude,  and  latitude  of  the  moon ; 

p.  A,  /?,  the  corresponding  co-ordinates  of  the  observer; 

r',  I',  b',  the  corresponding  co-ordinates  of  the  moon  as  seen  by  the 

observer; 
TT,  the  moon's  equatorial  horizontal  parallax;  and 


56 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


The  values  of  A  and  /?  are  obtained  from  the  observer's  geoceniric  longitude  and 
local  sidereal  time  by  changing  the  right  ascension  and  declination  of  his  geocentric 
zenith  into  longitude  and  latitude.  If  we  take  the  earth's  equatorial  radius  for  unity 
of  distance,  the  value  of  p  may  be  taken  at  once  from  geodetic  tables,  or  computed 
from  well-known  formulaj.     Putting 

q>',  the  observer's  geocentric  latitude; 

T,   his  sidereal  time  expressed  in  arc; 

aj,  the  obliquity  of  the  ecliptic, 
compute  u  and  W  from  the  formula? 

k'  sin  M  =  p  sin  q>'; 

111  cos  u=.  p  cos  ip'  sin  r. 

Then,  p  cos  ft,  p  sin  yff,  and  K  are  given  by 

'    ■  p  cos  ft  cos  A  =:  /o  cos  <p'  cos  r; 

p  cos  yff  sin  A  =  k'  cos  (m  —  a?)  =  cos  m  p  cos  tp'  sin  r  +  sin  g>  p  sin  <p'; 
p  sin  /S  =.  k'  sin  (m  —  a>)  —  cos  a?  p  sin  <p'  —  sin  oo  p  cos  tp'  sin  r. 

A  partial  check  on  the  accuracy  of  the  computations  may  be  obtained  by  comput- 
ing sin  fi  and  cos  /?,  and  noting  that  the  two  correspond  to  the  same  angle;  but,  as  this 
quantity  is  not  needed  separate  from  p,  I  have  prefen-ed  to  depend  on  duplicate  com- 
putation by  different  computers.  It  may  be  remarked  that  5-place  logarithms  are 
always  ample  in  this  computation,  and  that  tlu;  error  from  neglecting  the  nutation  of 
the  obliquity  of  the  ecliptic  can  never  exceed  o".i5  in  the  apparent  place  of  the 
moon. 

Taking  the  earth's  equatorial  radius  as  unity,  which  gives 

r  sin  w  =  I, 
we  have  the  three  equations: — 

B  cos  b'  cos  I'  -zz  cos  h  cos  I  —  p  cos  fi  sin  tt  cos  A. 

R  cos  V  sin  /'  =  cos  h  sin  i  —  p  cos  /?  sin  ar  sin  A.  (i) 

B  sin  V  =:  sin  6  —  p  sin  13  sin  tt. 

Let  a  be  any  arbitrary  angle.  If  we  transform  thf  first  two  equations  into  the 
two  others, 

(i)  X  cos  a  +  (2)  X  sin  «, 
—  (i)  Xsin  «  +  (2)  Xco8«, 
they  will  be: — 

B  cos  h'  cos  {V  —  a)z=.  cos  h  cos  {I—  a)  —  p  cos  (3  sin  tt  cos  (A  —  a). 
B  cos  V  sin  {V  —  a)z=. cos  h  sin  {I—  a)  —  p  cos  ft  sin  ir  sin  (A  —  a\ 

If  we  suppose  a  =:  A,  they  will  be: — 

B  cos  V  cos  {V  —  A)  =  cos  h  cos  {l—X)~p  cos  ft  sin  tt. 
B  cos  h'  sin  Q!  —  A)  =  cos  h  sin  (l  —  A). 

Apart  from  the  number  of  decimals  required,  these  equations  are  tlie  most  simple. 
They  give  R  cos  V  and  V  —  A,  while  the  third  of  equations  (i)  gives  li  sin  V,  whence 
V  and  B  are  obtained.     They  require,  however,  the  full  number  ol  decimals  requisite 


(■2) 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


57 


to  determine  a  large  angle  with  the  required  degree  of  accuracy.     Since  X  may  be 
known  only  to  o'.i,  while  I  —  \  must  bo  known  to  o".i,  it  is  necessary  to  see  that  the 
same  value  is  subtracted  from  I,  and  then  added  to  I'  —  A, 
If  we  suppose  or  =  /,  the  equations  will  be: — 

B  cos  b'  cos  (I'  —  ?)  =  cos  6  —  p  cos  fi  sin  tt  cos  {I  —  A). 
B  cos  h'  sin  (I'  —  I)  =zp  cos  /3  sin  tt  sin  (I  —  A). 

These  equations  have  the  advantage  of  requiring  only  6-place  logarithms. 

Having  thus  .obtained  jB,  h',  I'  —  I  or  I'  —  A,  and  thence  I',  the  apparent  semi- 
diameter  of  the  moon,  or  s',  is  found  from  the  equation 

k  sin  TT 


(3) 


sui  s  =: 


R 


k  being  the  ratio  of  the  diameter  of  the  moon  to  that  of  the  earth.  The  semidiameter, 
s',  is  so  minute  that  we  may  suppose  it  equal  to  its  sine,  making  the  equation  for 
its  determination,  in  seconds, 

o'_  [5-31443]^  sin  a-, 

The  value  of  k  which  we  shall  adopt  is  that  of  Qudemans,*  0.27264.     Tliis  will  give: — 

log*  =  9.43559. 

,'_  [475002]  sin  5 
_  ^^  .  .       . 

2. — A2H)arent  Place  of  the  Siai  or  Star, 

If  the  phenomenon  is  an  eclipse  of  the  sun,  the  position  of  the  sun  is  derived 
immediately  from  the  tables.  It  must,  however,  bo  corrected  for  parallax.  Owing  to 
the  minuteness  of  this  correction,  and  the  near  apvjroach  of  the  centres  of  the  sun 
and  moon  during  any  phase  of  an  eclipse,  it  will  be  sufficient  to  8ul)tract  the  horizontal 
parallax  of  the  sun  from  that  of  the  moon,  to  use  this  difference  instead  of  a-  in  tlio 
preceding  formula;,  and  then  to  apply  no  correction  to  the  place  of  the  sun  on  account 
of  parallax. 

In  the  case  of  a  star,  the  longitude  and  latitude  are  to  be  reduced  to  the  dat(; 
of  the  observation  by  applying  precession,  proper  motion,  nutation,  and  aberration. 
If  we  put 

«,  the  rate  of  motion  of  the  polo  of  the  ecliptic  on  the  celestial  sphere  ; 
y,  the  longitude  of  the  point  toward  which  it  is  moving ; 
T,  centuries  after  1800;  and 
T',  centuries  after  1850, 
the  resulting  rate  of  change  of  the  longitude  and  latitude  of  a  star  arising  from  the 
motion  of  the  ecliptic  alone  will  be: — 

In  longitude,  «  tan  li  sin  {L  —  y). 
In  latitude,     «  cos  (L  —  y). 
These  expressions  being  independent  of  the  equinox  of  roferonco,  we  may,  in  them, 
suppose  both  L  and  y  to  bo  refen-ed  to  a  fixed  equinox. 


"Aslniiomische  Nachrichtcn,  Ud.  li,  45. 


-75  AF.2 


58 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


In  reducing  the  star-places  to  the  ecliptic,  Hansen's  oblicpiity  will  be  used,  the 
value  of  which  is: — 

«=::23°2  7'54".8o-46".78T. 

Adopting  this  change  of  obliquity,  as  I  have  done  in  my  Inrcsti(/at'mi  of  the  Orbit 
of  Uranus,  where  the  motion  of  the  pole  of  the  ecliptic  in  the  direction  of  the  vernal 
equinox  of  1850  is  $".43  T  -f  o".i9  T'*,  and  that  in  the  direction  of  90°  greater  longi- 
tude is  46". 78  T  —  o".o6  J?"*,  we  find,  taking  the  century  as  the  unit  of  time,  and  count- 
ing from  1 800, 

K  =  47".09  —   o".09  T, 

r=:  83°  23' -28' 2"; 

;'  being  here  counted  from  the  fixed  equinox  of  1850.     Counting  from  the  equinox  of 
1800,  the  expression  will  be: — 

y  =  82°  s^'-28'  T. 

Taking  the  expressions  just  given  for  the  motion  in  longitude  and  latitude,  when  the 
equinox  is  fixed,  namelv, 

(IL 


(IT 


=  K  tan  li  sin  (Z  —  y), 


^j,z=x  cos  (L  —  y), 

we  find,  by  differentiating  and  substituting  the  numerical  values  of  the  centennial 
variations  of  «  and  y, 

(PL 

-jfpi^  zz  \  n^  sec*  B  sin  2  (L—y)  —d'.og  tan  B  sin  {L—y)  +  28'  h  tan  B  cos  {L—y). 

In  the  case  of  occulted  stars,  the  maximum  value  of  this  expression  is  about  o".04,  and 
the  corresponding  effect  on  the  longitude  of  the  star  is  o".02  T';  it  may,  therefore,  be 
entirely  neglected.  For  the  secular  variation  of  the  motion  in  latitude,  we  have, 
neglecting  insensible  terms, 

-^=  —  o".09  cos  (Z  —  7/)  —  28'  «  sin  (Z  — ;/) 
=  —  o".09  cos  (i  —  y)  —  o".38  sin  (Z  — ;') 

•  -      o".39sin(Z-;)/+i94°). 

The  proper  motion  in  longitude  and  latitude  may  be  derived  from  those  in  right 
ascension  and  declination  by  the  well-known  formula}  for  converting  changes  of  the 
one  system  of  co-ordinates  into  those  of  the  other.     If  we  put 

//,  /<',  )U„  //g  the  proper  motions  in  right  ascension,  declination,  longitude,  and 

latitude  respectively ;  and 
E,  the  complement  of  the  angle  at  the  star  of  the  triangle  formed  by  the  star 
and  the  poles  of  the  equater  and  ecliptic, 
we  shall  have : — 

cos  i^  rr  sin  w  cos  a  sec  J?  zz  sin  qj  cos  L  sec  6. 

//,  =  yu  sin  E  cos  8  sec  B-\-  n'  cos  E  sec  B.  (4) 

yUj  =  —  //  cos  JE  cos  8-\-  fi'  sin  E. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


m 


Owing  to  the  extreme  slowness  with  whicli  the  position  of  the  ochptic  changes,  //,  and 
1^2  may  bo  supposed  constant,  which  is  not  tlio  case  with  jn  and  /i'. 

Collecting  the  various  terms  in  the  motion  of  the  star  which  we  have  deduced,  and 
including  precession,  we  find  that  its  loiigitude  and  latitude,  at  the  epocli  T  centuries 
after  1800,  refen-ed  to  the  equinox  of  the  epoch,  is  : — 


(5) 


(6) 


L  =  Lo  +  L'T+L"T-; 
V  =  Iio+B'T-{-B"r; 
whore  we  put 

La,  Bo,  the  longitude  and  latitude  for  1 800.0 ; 

Yo  =  82°  55'; 

L'  =Mi+  5024".!  I  +  47"- 14  tiin  ^0  sin  (-^0  —  ?'o); 
■L"  =  i".i3; 
7?' =  )Ua  +  47"-i4  cos  (Zo  —  Xn)  ; 
li"  z=  o".20  sin  (Lo  - n  +  1 94°)- 
If  we  count  L^,  B^,  and  Xo  from  the  equinox  and  ecliptic  of  1850,  and  T  from 
the  epoch  1850.0,. the  same  expressions  will  hold  by  putting 

yo  =83°  23': 

L'  z=.  /<i  +  5025".24  +  47".09  tan  B^  sni  (Zo  —  Xo); 

r'=i.i3;  (^') 

J5' = //g  +  47"-09  cos  (Xo  —  Xo); 

B"  =  o".20  sin  {Lo  -  n  +  i94°)  =  o"-20  sin  {Lo-  m  °). 

Having  thus  obtained  the  mean  position  of  the  star  for  the  required  epoch,  the 
apparent  position  is  obtained  by  applying  nutation  and  aberration.  But,  if  the  former 
correction  be  omitted  from  the  place  of  the  moon,  it  may  U  omitted  froni  that  of  the 
star  also.     This  course  has  been  adopted.     The  coirection  for  aberration  is:— 

<5i  —  —  2o".45  sec  .7?  cos  (0  —  i) ; 
SB  —  —  2o".45  sin  B  sin  {Q  —  L); 

the  symbol  ©  representing  the  sun's  true  longitude. 

^  ^.— Distance  of  Centres  of  the  Two  Bodies. 

Having  found,  by  the  preceding  methods, 

L,  B,  the  longitude  and  latitude  of  the  star  or  sun, 
I',  h',  s',  the  longitude,  latitude,  and  semi-diameter  of  the  moon, 
the  distance  of  centres,  D,  and  the  angle  of  position,  m,  of  the  line  jo.hiing  the  cen- 
tres are  given  by  the  equations : — 

sin  i  I>  sin  m  —  sin  \  (/'  —  i)  V  coslTcoa  77; 
sin  \  D  cosmzz  sin  A  (b'  —  B)  ; 

the  angle  m  being  counted  from  the  south  point  of  the  moon's  disk  toward  the  west. 

Wo  have  also  ,         ^        .<,,.,,      T>^ 

cos  b'  COS  B  =z  cos*  i  {V  +  /»•)  -  sm*  i  ('''  -  '0- 


6o 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Since  the  last  term  of  this  equation  can  never  amount  to  ;^,  wo  may  substitute 
eoH  ^  (J/  -f  J})  for  V  COS  b'  cos  li  in  the  first  of  equations  (6).  Wo  may  also  dotermino 
])  and  m  with  all  necessary  accuracy  from  the  approximate  equations, 

•  Ds\nm=:(l'-L)  coa^(b'-{-Ii),  . 

Dcosmzzh'  —  B.  ' 

Tiie  error  in  this  determination  of  m  will  bo  of  no  importance,  because  this  angle 
i»  never  observed  with  such  accuracy  as  to  be  used  as  a  datum  for  con-ecting  the 
moon's  place,  while  tho  error  in  B  is  so  small  as  to  bo  entirely  unimportant.  In  fact, 
if  we  represent  by  B'  the  approximate  value  of  B  derived  from  (7),  wo  have : — 

D"  =  (r  -  z)"  cos«  i  (^' + -B)  +  (^' -  ■»)'; 

while  developing  tho  sines  of  J  2>,  i  Q'  —  L),  and  i  (6'  —  B)  in  the  rigorous  equation 
to  quantities  of  the  third  order,  we  have : — 

sin  JD  =  JD  A  -j-^'^y 

m^  ^{l'  -L)  =  ^  (l'  -  L)  (^1  -  ^{l'  -Lyy 

sin  i  (fc' -  «)  =  Hi' -  ^)  (i  -  74  («*' -  ^)')- 

Substituting  those  values  in  the  rigorous  equations,  and  taking  the  sum  of  the  squares 
of  tho  two  equations,  we  find 

2)'=(Z' - Lf  cos'  i  (b'+B)-\-ib'  - Bf  +  ^  (2>* -  ^l*  cos"  i  {V  -{-B)-  Jb* ), 

where  we  have  put,  for  brevity, 

Jl-V  -L; 

Jb  =  b'-B. 

Substituting  the  above  value  of  B",  we  have 

(D  -  B')  {B  +  D')  =  n  ^^*  ~  ^'*  *'^^'  ^  ^^'  +  -^)  -  ^^')' 
showing  that  the  maximum  value  of  D  —  B'  is  43  B^,  or  less  than  o".oi.     The  equa- 
tions ( 7)  are  therefore  exact  enough  for  all  practical  purposes. 

4. — Equations  of  Correction. 
If  all  the  elements  of  reduction  were  correct,  we  should  have,  in  case  of  an  occul- 
tation,  tho  value  of  B  from  (7)  equal  to  that  of  s'  from  (4).  Wo  have  now  to  find  the 
equation  of  condition  which  must  subsist  among  the  corrections  to  tho  lunar  elements 
in  order  that  we  may  have  B  =  s'.  Owing  to  the  minuteness  of  these  corrections, 
their  coefficients  need  not  bo  accurate  to  more  than  two  significant  figures;  wo  may 
therefore  suppose  cos  .J  (b'+B)  to  be  equal  to  unity,  since  its  minimum  value  exceeds 
0.995.     If  tli6"  ^^  P"*>  ^'^^  brevity, 

a;  =  (i'  -  i)  cos  J  {V  +  B), 
y=zb'-B, 
J  {b'  -j-  B)  differs  so  little  from  6  that  we  may  put 

Sx  =  (SI'  —  6L)  cos  6, 
Sy  =  Sb'  —  SB; 


from  which 


RESEARCHES  ON  THE  MOlION  OF  THE  MOON. 


6D  =  {,61'  —  SL)  cos  h  sin  m  +  {SV  —  SB)  cos 


6i 


m. 


(«) 


(9) 


Lot  US  now  rofor  to  the  equations  (i)  and  (3).     If  wo  put,  for  brevity, 

p  =  p  cos  fi  sin  TT, 
qzz  p  sin  /3  sin  tt, 

we  have  from  (3)  and  (i)  • 

i      /;/      A  P  sin  (J  —  ^) 

tan  (I  —l)  =  — ^ — -^ /r — T\' 

^  cos  b  —I)  cos  (,« —  A) 

J?  sin  y  =  siii  &  —  (7. 

Tlio  angle  /'  —  I,  or  the  parallax  in  longitude,  is  so  small  that  wo  may  suppose  it 
equal  to  its  tangent, while  the  denominator,  cos  h  —  p  cos  {I  —  A),  is  always  contained 
between  the  limits  0.98  and  unity.  Again,  the  quantity  11  is  always  contained  between 
the  limits  0.982  and  unity.  Wo  may  then  put,  without  an  eiTor  of  more  than  one 
hundi'edth  in  the  coefficients. 


I'  —  Izzi.oi  p  sin  {I  —  A), 
sin  ^'  =  4  (sin  ^  —  Q)- 


(10) 


From  these  equations  we  obtain 

81'  =\i-\-  i.oi  p  cos  il—\)\6l-\-  i.oi  m\{l—X)Sp—  i.oi  p  cos,{l—\)  6X; 
and,  putting  cos  h  and  cos  V  equal  to  unity, 


dV  =  I.OI  Sh  —  i.oiSq  —  ^^  (sin  b  -  q)  6It. 


(II) 


Owing  to  the  minuteness  of  p,  q,  Sb,  Sj),  and  6q,  the  factor  i.oi  may  be  entirely 
omitted  in  the  above  expressions.  We  have  next,  from  (9),  putting  cos  ff  equal  to 
unity: — 

6 p  —  p  coa  fi  Stt  —  q  Sft. 

6  q  zz:  p  sin  fi  Sff  +  p  6/3. 

The  longitude  and  latitude  of  the  observer's  geocentric  zenith,  A  and  0,  are 
functions  of  his  lat^Uide  and  of  the  local  sidereal  time.  The  former  must  be  supposed 
to  be  known;  but  the  variation  of  the  latter  may  be  taken  into  account  in  order  to 
determine  the  effect  of  an  error  in  the  time  of  observation  upon  the  lunar  elements. 
The  most  simple  formulae  for  expressing  errors  of  longitude  and  latitude  in  terms  of 
the  errors  of  right  ascension  and  declination  are  those  of  Gauss,  in  his  Theoria  Motus 
Corporum  Coelesfmm,  §  68,  and  are  these : —Determine  the  angle  E  between  0°  and 
1 80°  from  the  equation 

cos  E  zn  sin  CO  cos  r  sec  /?  =  sin  00  cos  A  sec  gi'. 

Then 

SX  =  CCS  <p'  sin  E  sec  /3  St  +  cos  E  sec  ^6g>', 

S/3  zz  —  cos  g>'  cos  E  Sr  +  sin  E  Sq>'.  ' 


52  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

The  l(i8t  term  in  each  equation  is  included  only  for  the  sake  of  completeness  in 
writing.     The  substitution  of  this  value  in  dp  and  Sq,  neglecting  Sq)',  gives  :— 

Sj)  zz  p  co»  /3  6 TT  -{-  q  cos  q)'  cos  J'j  St. 
6q  =.  p  sin  ft  Sir  —  p  cos  q}'  cos  E  St. 

The  correction  to  the  tabular  ecliptic  longltudo  is  represented  by  SI.  For  the 
sake  of  completeness,  we  shall  suppose  the  local  mean  time  of  observation  to  require 
the  correction  St,  and  the  west  longitude  of  the  piano  to  require  the  correction  S\'. 
We  shall  then  have,  for  the  total  con-ection  to  the  moon's  geocentric  longitude  and 
latitude, 

Sl-\-{St+  SX'Y^^, 

sb  +  {st  +  sr)^, 

which  are  to  be  substituted  for  SI  and  <56  in  (i  i). 

By  taking  the  square  root  of  the  sum  of  the  squares  of  ecpiations  (i),  neglecting 
terms  of  the  second  order  with  respect  to  the  parallax,  we  find: — 


Hence 


E=:i  —p  cos  h  cos  (l—X)  —  q  sin  b. 

SB=z  —  cos  b  cos  {I  —  X)  Sp  —  sin  b  Sq -{- p  cos  b  sin  {1  —  \)  (SI  —  SX) 
+  (ps,\nbcos{l—X)  —  qcosb)Sb; 


or,  by  substituting  for  Sj),  Sq,  and  SX  their  values, 

SB  =  p  cos  b  sin  {I  ~X)Sl+  (p  sin  b  cos  {l  —  X)~q  cos  b)  Sb 

+p  cos  q>'  sin  tt  {cos  fi  cos  E  sin  6— sin  E  cos  b  sin  (l—X) 

—  sin  13 cos  E cos  b  cos  {1—X)\St  —  p  (cos  ft  cos  b  cos  (i  —  A)  +  sin  /? sin  b)  Stt 

In  these  several  equations,  t  is  the  sidereal  time  expressed  in  arc ;  and,  by  taking  for 
the  unit  of  time  that  in  which  the  earth  rotates  through  unity  of  arc,  we  may  suppose 
St-zST.  If  wo  substitute  these  several  expressions  in  (u),  omitting  the  factor  .oi, 
which  renders  the  terms  in  which  it  occurs  unimportant,  omitting  also  the  terms  which 
contain  sin  b  sin  7t  or  sin'  b  as  a  factor,  we  find : — 


<5/'  =  { 1  +j>  cos  {l—X)\  Sl+  \i+p  cos  {I- 


x)i'l,r 


+  {  [i  -\-p  cos  (/  —  A)  ]  1:  +  p  cos  q>'  sin  tt  [sin  /?  cos  E  sin  {l  —  X) 
-sinJJcosC^-A)]  \St  +  p  cos /?  sin  (Z  -  A)  (J;r.  (12) 


SV  =  <56  + 


at      ^\ 


db 
di 


~\-  p  cos  q>'  cos  E  \  St 


) 


+  { sin  &  cos  /?  cos  b  cos  (i  —  A)  —  sin  /?  |  p  Stt. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


63 


The  coefficients  of  Stt  iii  tlioso  equations  nmy  be  obtftined  with  {greater  ease,  and 
with  ample  accuracy,  from  the  expressions : — 

ill'  _l'-l 

drr  ~     7C    '  * 

dh'  _  //- i 
dn  ~     Tt    ' 

Our  next  step  will  bo  to  substitute  the  corrections  of  the  moon's  lon<>itudo  in  orbit 
and  of  the  position  of  the  plane  of  the  orbit  for  those  of  the  ecliptic  longitude  and 
latitude.     Let  us  put  , 

1',    the  moon's  longitude  in  orbit,  counted  from  a  departure  point  in  tiio  orbit ; 

0,   the  longitude  of  the  node ; 

as,  the  longitude  of  the  perigee ; 

?,    the  inclination  of  the  orbit ; 

«,    the  argument  of  latitude ;  and 

/?',  a  latitude  counted  in  a  direction  perpendicular  to  the  plane  of  the  orbit: 

the  ecliptic  longitude  and  latitude  will  then  be  given  in  terms  of  «,  0,  and  i,  by  the 
equations 

tan  {l—O)  =  cos  i  tan  », 
•  .    ,        ... 

sni  t»  =  sm  t  sm  w ; 

whence  wo  derive,  for  the  differential  variations, 

cos  I  81  —  cos  h  8d  -\-  sec  h  cos  i  Su  —  sin  \)  cos  (/—  0)  Si, 
cos  b  Shz=.  sin  i  cos  u  Su  +  cos  i  sin  m  di. 

As  we  have  defined  v  and  /3',  their  vai-iations  are  given  by  the  equations 


6v  =  Su  +  cos  i  SO, 
S/S'  =  sin  u  Si  —  sin  i  cos  u  SO. 


(13) 


The  relation  of  these  four  equations  is  such  that  cos  b  SI  and  Sb  admit  of  being 
expressed  as  functions  of  Sv  and  <J/?'  simply. .  The  equations  for  this  purpose  are  :— 


cos  b  Sl=:  —  ^  Sv  —  sin  i  cos  (I  —  0)  Sfi'. 
cuso 

Sb  -  sin  I  cos  (?  -&)Sv^  ^—,  8/3'. 
^  cos  0 


(14) 


In  fact,  by  substituting  in  these  equations  the  values  of  Sv  and  So'  from  (13),  we 
shall  reproduce  the  expressions  for  cos  b  SI  and  cos  b  Sb  just  given. 
If  we  determine  an  angle  a  by  the  equation 

sin  a  =  sin  t  cos  (l  —  Q), 

we  shall  have 

cos  i 


cosb 


z=  cos  « ; 


64 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


(IS) 


and  a  will  then  bo  tho  nnglo  which  tho  moon's  orbit  makes  with  tlio  parallel  of  lati- 
tude. 

If  in  ( 1 2)  wo  put,  for  brevity, 

I  +  j;  COS  (i  — A)  =/, 

tho  quantity  /  will  bo  so  near  nnity  that  wo  may  suppose  6h  to  bo  multiplied  by  it 
without  any  sensible  error.  Taking,  next,  so  much  of  tho  expression  for  SD  in  (8)  as 
depends  on  tho  place  of  the  moon,  namely, 

SD  =  cos  b  SI'  sin  »»  +  Sb'  cos  m, 
if  wo  substitute  for  «5/  and  Sb'  the  terms  of  (12)  which  depend  on  61  and  Sb,  wo  find 

SD  —f  (sin  m  cos  b  61  +  cos  m  6b); 
while  substituting  tho  angle  a,  (14)  become 

con  b  61  z=.  cos  a  6v  —  sin  a  Sfi', 
6b  =  sin  a  6v  -\-  cos  a  6 ft'; 

whence  wo  derive 

6D=f\  sin  {m  +  a)  6v  +  cos  (»»  +  a)  6fi'  \ . 

If  wo  substitute  for  6v  and  6ft'  their  values  in  (13),  wo  shall  have 
SD  zzf  \  sin  (>»  -\-a)  Su,-\-  cos  {m  +  a)  sin  u  6i 

4-  [cos  i  sin  (»i  +  «)  —  sin  i  cos  (»i  +  a)  cos  m]  50  ^ 
Representing  tho  moon's  mean  longitude  counted  in  the  usual  way  by  f,  wo  shall 
have 

Q  representing  tho  equation  of  the  centre  and  the  other  inequalities,  and  being  a  func- 
tion of  f,  ai,  and  0,  and  of  tho  sun's  mean  longitude,  which  we  represent  by  e'.  Wo 
then  have: — 

dv        (   ^'^Q\,„''^Q,'^^  dm     dQ  d9 
di  =  ''y'^de)^      de'  +  d^-'dt-^ded'f 

Owing  to  tho  minuteness  of  the  terms  of  E  which  contain  «',  as  well  as  of 

d(3       -,  dd  . 

-,-  and  -,;,  we  may  put 
dt  dt 

de~         de  ~  n'  dt' 

without  an  error  of  more  than  —  of  tho  whole  expression.     Wo  have  also,  with  sufli- 

500 


(16) 


cient  accuracy. 


dJl__ 


doo 


z=  —  2ecoag; 


g  being  tho  moon's  mean  anomaly.     The  coefficient  J^  may  be  omitted  entirely.   Sub 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  65 

Btituting  ill  ( 1 5)  the  value  of  fift'  from  ( 1 3),  luul  tliat  of  <5r  from  ( 1 6),  after  makiiifr  tlio 
Hu1)8titiitionH  just  indicated,  we  find 

^lizzfX  sin  (m  +  «)  ^'  .  |^J  (54  —  2  nin  (/«  +  a)  com  //  v.  '5w  +  com  («i  +  a)  sin  if  di 

—  COH  (/»  4-  o")  c»»n  '«  sill  «  <5(9  >, 

In  the  use  of  this  formula,  '    nmy  be  Hiilhstitiited  for  ' '',  owintr  to  the  comparative 
minutenosH  of  the  difference  between  the  two  exjjresHions. 

Next,  to  find  the  value  of  -.    or    -  ,  we  .substitute  the  projier  terms  (if  (12)  in  (^8). 
From  the  latter  we  have 


—.7-  =:  sm  m  cos  b 
dt 


\  dt       dt ) 


+  cos  m 


dh' 
7lt' 


and  from  the  former,  omitting  the  factor /=  i  -{-  p  (uis  (/  —  A), 

.,  z=.  +  p  cos  ip'  sin  TT  \m\  /3  cos  1'J  sin  (/  —  A)  —  sin  U  cos  (/  —  A)  |, 

db'     dh   ,  ,         „ 

,7  =  „  +  p  cos  <»  cos  i. 
dt      dt 


For  the  terms  of    .-,  independent  of  the  moon's  parallax,  we  find,  willi  sufficient 

approximation, 

dv    .     ,      ,      ^  dl   .     ■      .      . 

J-  sm  (m  +  a),  or  ,^  sm  1  in  +  a), 

dt         ^  ^  dt  ^ 

For  the  other  terms,  wo  determine  the  tpiantities  //  aiul  tj)  by  the  equations 
cos  h  =z  cos  /3  cos  E  =  sin  oj  cos  r ; 
sin  h  sin  {if>  —  X)  =.  sin  Jv; 
sin  h  cos  (^i*  —  A)  zr  sin  /?  cos  i:,'. 

The  angle  h  is  to  be  taken  between  0°  and  180°,  so  that  sin  h,  like  sin  it,',  is 
always  positive.     With  this  restriction,  ip  —  A  may  be  obtained  from  the  foi-mula 

.       /  /       -1  \       tan  E 
tan  (0  — A)  =:-.- 

sm  /^ 

The  angle  ^  — A  must  therefore  be  included  between  the  same  limits.     If  we  omit 
the  factor  cos  b,  the  terms  which  depend  upon  the  parallax  now  become : — 

p  cos  Ip'  sin  TT  (sin  h  sin  m  sin  (l  —  ip)  +  <J08  h  cos  /»). 
The  entire  expression  for      -  now  bec^omes 

-     =  ^  sin  {m  +  a)  H  P  cos  ip'  sin  r  (sin  /«  sin  m  sin  (/  —  i/>)  +  cos  A  cos  m)  —  --  sin  /«. 
dt       lit  dt 

h,  being  a  function  <>f  <•  simply,  aiul  independent  of  the  place  of  observation,  may 
be  tabulated  with  t  as  the  argument. 
9 75  AP.2 


66 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


For  the  coeflficients  depending  on  the  longitude  of  the  pUice,  we  have 
for  which  we  may  put 


For  the  coefficient  in  respect  to  the  paralhix,  we  have 

dn-  TT  IT 

Li  those  of  the  precedin.r  expressions  which  depend  on  tiie  adopted  unit  of  time, 
it  will  b«>  remembered  that  this  unit  is  tacitly  supposed  equal  to  the  time  in  which  the 
earth  rotates  through  the  radias  imit  of  arc,  or 

24  sidereal  hours 


in 


or. 


In  sidereal  time,  13751"=  229'".2  =  3\82; 
In  mean  time,    13713' =  228'".6  =  3\8i. 

Numerical  factors  will  be  roipiired  when  the  si  cond  is  taken  as  the  unit  of  arc. 

The  t".)rnml!«  to  be  actually  employed  in  the  computations  nniy  now  be  recapitu- 
lated as  fo.lcws : — 

(A  From  the  geocentric  latitude  of  the  place,  <p',  and  the  sidereal  time  at  Avhich 
an  occultation  was  observed,  t,  compute  the  ecliptic  co-ordinates  of  the  observer,  A, 
p  sin  fi,  anl  p  cos  /?,  by  the  formuhe: — 

p  cos  /?  cos  A  =  p  cos  cfl  cos  T, 
p  cos  fi  sin  \z=.y  cos  (m'  —  co\ 
p  sin  li  —  y  sin  (»'  —  <»)  ; 

the  quantities  V  and  «'  being  firsi  iletermined  from  the  equations 

V  sin  «'  =p  sin  (p\ 
k'  cos  h'  ■=z  P  cos  (f>  sin  r. 

Five-place  logarithms  are  always  sufficient  for  this  computation. 

(2)  Tut 

])  ■=  p  cos  /3  sin  T, 
*  H  z=.  p  sin  /?  sin  w; 

and  compute  i^  /',  V ,  and  s'  from  the  equations 

11  cos  h'  sin  (/'  -l)=P  sin  {I -  A), 
H  cos  y  cos  (/'  —  0  =  t-os  h—p  cos  (/  —  A), 
li  sin  //=:sin  h  —  q, 

,  __  [4.75002]  sin  TT 


RESEARCHES  OM  THE  MOTION  OF  THE  MOON. 


67 


jf,  b,  and  tt  being  tlie  tabular  geocentric  longitude,  latitude,  and  parallax  of  the  moon 
for  the  moment  of  observation.  Here  5-place  logarithms  ai'e  enough  for  terms  having 
sin  /T  as  a  factor,     i^lsewhere,  6  are  required. 

(3)  Having  found  the  apparent  longitude  and  latitude,  L  and  B,  of  the  eclipsed 
sun  or  occidted  star,  find  D  and  m  from  the  equations 

D  sin  m  =  (I'  —  L)  cos  J  (h'  +  Ii), 

D  cos  m  zzh'  —  B,  ;    .■  v  '■_,[' 

using  5-place  logarithms.     In  the  coniputati»ms  of  the  difterential  coefficients  which 
follow,  3  places  are  sufficient. 

(4)  Find  the  angles  E,  i(>  —  A,  and  /(,  all  between  0°  and  180°,  from  the  equations 

cos  E  zz  sin  co  sec  /3  cos  r, 
cos   A  rr  sin  QJ  cos  r,  /        V 

,      .  ,       .V      tan  E 
^  svn  /y 

For  any  one  place,  these  angles  ma}'  all  be  tabulated  as  a  function  of  t  ;  and  the 
values  of  sin  h  and  cos  /«,  being  indejiendeiit  of  the  latitude,  will  answer  for  any  place 
whatever. 

(5)  Find  cc  from  the  equation 

a  =z  5^.14  sin  », 
which  ma}'  be  tabulated  as  a  function  of  it. 

(6)  Put  (/')  for  the  motion  of  the  moon's  geocentric  longitude  in  o^oi,  expressed 
in  minutes  of  arc.     Then 

'//'_.(0.  ->:-:•■  ;:,--::^;-  ,     ': 

de      7.90' 

(7)  Find  the  moon's  mean  anomaly,//.  Wiien  Hansen's  tables  are  employed, 
the  disturbed  anomaly  may  be  used,  and  found  by  the  formula 

,7=i3".o65(.'-i5.i8). 

(8)  The  several  differential  coefficients  which  admit  of  being  determined  from 
the  eclipse  or  occultatiou  are  then  as  follows : — 

de      f/e 


dh 

f  du) 

dp 
idd 


=:  ~  2  cos  //  sin  (/»  +  '•')> 
=:  —  cos  H  cos  {m  -f  a). 


dJ)         .  /       ,      ^ 

,.  i::sni  11  cos  (111  +  a), 
di 

-    -  =z  sni  w  +  "         cos  in. 

dir         TT  /T 


68 
dfi' 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


■J  rr  cos  (»i  -f-  a). 


dt       14.4        ^  ^ 


+  15.05  /3  COS  ^'  sin  ;r  {sin  h  sin  wi  sin  (/  —  ';&)  +  cos  h  cos  >»}  —  > — -*  sin 


»n. 


';[!=z-('l)-sinO«  +  a). 
f/A        14.4 

In  case  of  an  occullation,  tlie  equation  of  condition  will  be 

'^  5 e  +  i^  c  .565  +  etc.  =  s' -  7>. 
de  cdw  ' 

A  similar  fornuila  will  hold  for  eclipses  of  the  sun  computed  in  this  way,  except 
that  the  distance  of  centres  determined  from  the  observed  phase  must  be  substituted 
for  s'. 

$  7. 

EFFECT  OF   CHANGES   IN  THE   LUNAR   ELEMENTS   UPON  TUE   PATH   OF  TOE 

CENTKAL  LINE  OF  AN  ECLIPSE. 

Not  only  in  all  ancient  eclipses,  but  frequently  in  modern  ones,  the  data  derived 
from  observation  are  not  times,  but  the  lines  along  which  the  edge  or  some  point  of  the 
shadow  passes.  To  utilize  such  observations,  it  is  necessary  to  express  the  change  in 
the  central  line  due  to  changes  in  the  moon's  co-ordinates  or  elements.  This  I  have 
done  by  Bessel's  foraiuloe,  in  the  very  simple  form  in  which  they  are  developed  by 
Professor  PfiiROE  in  his  TrUjommctrij.     The  notation  is  as  follows: — 

A,  the  moon's  geocentric  longitude,  minus  that  of  the  sun  ; 
/?,  the  moon's  latitude,  diminished  by  that  of  the  sun,  if  necessary; 
e,  the  obliquity  of  the  ecliptic; 
)(,  the  angle  of  position  of  the  great  circle  drawn  from  the  centre  of  the  sun 

through  that  of  the  moon,  measured  toward  the  east  from  the  circle 

drawn  to  the  pole  of  the  ecliptic; 
Q),  the  angle  which  tiie  same  circle  makes  with  the  meridian  passing  through 

the  sun ; 
TV,  the  sun's  equatorial  horizontal  parallax  at  the  time; 
n,  that  of  the  moon  ; 

y,  the  angular  geocentric  distance  of  the  centres  of  the  two  bodies ; 
m,  the  ratio  of  their  linear  distances  from  the  earth's  centre ; 
c,  the  ansrular  distance  of  the  centres  of  the  earth  and  moon  as  seen  from 

that  of  the  sun  ; 
a',  d',  the  right  ascension  and  declination  of  the  sun  ; 
a,  d,  those  of  the  line  joining  the  centres  of  the  sun  and  moon ; 
L,  the  sun's  longitude. 


69 


(0 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

We  then  have : — 

tan  y  sin  M  =  tan  A. 

tan  y  cos  u  zz  tan  /3  sec  A. 

sin  ;r 
sin  11 
c  zz  206265"  m  tan  y  cos  y. 
tan  (h  —  o))  z=  cos  i  tan  e.  •  ' 

rf  =  6'  —  c  cos  OJ.  / 

a  =  a' —  c  sin  GJ  sec  (5'. 
Gj'  =  07  —  c  sin  CO  tan  6'.  ' 

j^_sin(y-fc) 
sin  // 

The  co-ordinates  of  the  point  in  wliich  the  centre  of  the  shadow  intersects  the 
plane  perpendicular  to  it  passing  through  the  centre  of  the  earth  will  bo,  when  reck- 
oned in  the  usual  way: — 

X  z=  li  sin  co' .  "  ,.. 

y  zzlt  cos  CO . 
Next,  putting 

9>',  the  geocentric  latitude  of  a  point  on  tlie  earth's  surface  ; 
p,    its  distance  from  the  earth's  centre ;  ; 

/i',  the  west  hour-angle  of  the  axis  of  the  shadow  counted  from  the  meridian  of 
the  place ;  or, 

fi'  zz  sid.  time  —  «  =  apparent  time  +  <-"  si"  '^  sec  <5'; 

the  corresponding  co-ordinates  of  the  place  are  , 


H  z=.p  cos  (p'  sin  yu', 

ff=p  (sin  9>''cos  d  —  cos  <p  'sin  (/  cos  //'), 

^  =  p  (sin  gi'  sin  </  -f-  cos  ^'  cos  (/  cos  /<'); 

and  the  hourly  variations  of  the  first  two  are 

J?' =  [9.4192]  p  cos  ^' cos /«', 

//'  =  [9.4192]  p  cos  q)'  sin  d  sin  /t'. 

The  distance  of  this  placo  from  the  axis  of  the  shadow  at  any  time  is 


(3) 


VO'c-^)"" +  (//-'/)'■     ■  ,     • 

The  quantities  r,  H,  y,  and  ;;,  which  enter  into  this  equation,  arc  functions  of  the 
time  and  of  ti»e  elements  of  the  lunar  orbit.  The  datum  supposed  to  be  given  by  ol)- 
servation  is  the  least  distance  of  the  iilace  from  the  axis  of  the  shadow,  or  the  mininnun 
value  of  the  above  expression.  We  are  to  express  Ibis  minimum  value  in  terms  of  the 
tabular  elements  and  of  the  corrections  to  the  moon's  longitude  and  latitude  and  to 
the  longitude  of  the  sun.  To  conq)ute  the  tabular  mininuun,  we  are  supi^osed  to  be 
able  to  fix  a  time,  r,  so  near  it  that  the  difierontial  coefilcients  of  ^,  ?/,  x,  and  y  may  be 


70 


RESEARCHES  ON  THE  MOTION  OF  THE  \fOON. 


regarded  as  constant  during  the  interval  between  t  and  the  time  of  minimum  distance. 
We,  tlierefore,  suppose  that  for  a  time,  t,  including  the  moment  in  question,  we  have : — 

x  =  Xa-{-ocf  (t  —  T), 

y  =  yo  +  y'  (t-r),.  /n 

the  subscript  zeros  indicating  the  tabular  values  at  the  time  t.     Now,  putting,  for 
brevity, 

Y  =yo  —  Vuy 
Y'=v'-7,', 


(5) 


the  square  of  the  distance  of  centres  at  the  time  t  will  bo 
which  will  be  at  a  minimum  when 

__xx'-frr 

The  minimum  value  of  the  square  will  be  found  l)y  substituting  tliis  value  of  / 
the  preceding  equation,  and  is 

(XT-Xl")" 


T  in 


so  that  the  actual  tabular  value  of  the  minimum  distance  is 


J  = 


x'Y-xr 


(6) 


vx'-'+r"' 

which  is  positive  when  the  observer,  facing  in  the  direction  in  which  the  shado'v  is 
moving,  sees  the  axis  of  the  latter  pass  him  on  his  loft  hand.  As  the  .shadow  always 
moves  toward  the  east,  J  will  be  positive  when  tlie  axis  of  the  sliadow  passes  north 
of  the  place. 

The  minimum  distance  being  thus  expressed  as  a  function  of  tabular  quantities 
at  the  time  r,  the  change  of  this  distance  due  to  a  change  in  those  quantities  will  ex- 
press the  corresponding  change  in  the  i)ath  of  the  centre  of  the  shadoAv,  which  will  be 
positive  when  the  change  is  toward  the  north.  The  changes  to  be  considered  will  bo 
tliose  wliich  will  be  produced  fundamentally  l)y  small  clianges  in  the  latitude,  longi- 
tude, and  parallax  of  the  moon,  and  tlie  longitude  of  the  sun.  Omitting  the  subscript 
zeros  from  .r  and  y,  we  find,  from  the  equations  already  given. 


Sx  —  sin  oo'  61t  +  R  cos  co'  Sco', 
6y  —  cos  a)'  dll  —  R  %\n  to'  doo' . 


(7) 


The  quantity  c  is  so  minute  that  we  may  neglect  both  its  changes  and  the  tonus 
in  which  it  appears  as  a  frfctor.     ^Moreover,  /?,  y,  and  \  are  all  tfo  small  that  wo  may 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


n 


put  their  cosines  equal  to  unity  Avitliout  any  error  clianging  the  differential  coefficients 
by  their  thousandth  part.  . 

The  rigorous  value  of  (572  beiufj 

Sit  =  ^--.y.L-T'  (6y  -\-  dc)  —         )■  f^-^  cos// 0/7, 
sm  H      ^  m\*  II 

a  value  correct  to  its  four-hundredth  part  will  be 

ysn 


sni  n     snr  // 


(8) 


The  aDproximate  value  of  c  is    ■''  - ,  the  denominator  Ijeing  the  ratio  of  the  distances 
^^  400 

of  the  sun  and  moon  ;  a  farther  approximation  to  the  true  value  of  611  will  therefore, 

})e  obtained  by  increasing  the  right-hand  side  of  the  la.st  ecpiation  by  its  four-hundredtii 

part.     AVo  Iiave,  to  a  still  greater  degree  of  approximation, 

Say  z=.  <5cj; 

and,  by  differentiating  the  expression  for  (it  —  a>), 

So)  —  Sti  =.  tan  e  cos"  (»  —  &»)  sin  L  SL.  (9) 

The  maximum  value  of  this  term  is  0.4  6L.  The  probable  error  of  the  sun's  tabular 
mean  motion  does  not  exceed  i"  per  century ;  the  right-hand  side  of  tliis  equation  can, 
therefore,  scarcely  ever  amount  to  10"  during  historic  times.  The  greatest  error  in 
Sx  and  61/  which  can  arise  from  omitting  it  will  therefore  be  of  the  order  of  niagni- 
tutlo 

M  X  10"  or  -^. 

20000 

The  maximum  value  of  II  being  about  4000  miles,  the  corresponding  error  in  the 
path  of  the  shadow  will  bo  less  than  400  yards  fitr  the  most  ancient  eclipses,  and  less 
than  50  yards  for  tlio    lodern  ones.     It  may  therefore  be  entirely  omitted,  which  will 

make 

dcoziiSu. 

Wo  have  thus  made  the  variations  of  :c  and  y  to  depend  on  those  of  11,  y,  and  /I  by 
the  equations  (7),  (8),  and  (9).  We  have  next  to  express  the  variations  of  u  and  y 
in  terms  of  the  variations  of  the  elenients  on  which  they  depend.  Since  we  suppose 
cos  y,  cos  A,  and  cos  /?  to  be  sensibly  unity,  we  find,  by  differentiating  the  first  two  of 

equations  (i), 

m\  u  6y -\- y  co9,nSuzz.S\, 
com  Sy —  y  mxudn-zzSft;         i 


Avhich  give 


f>y  —  sin  !<  <5A  -f  cos  M  6ft, 
y  6uzz  COS  ^^6\  —  sin  m  6ft, 


T2 


RESEARCHES  ON  THH  MOTION  OF  THE  MOON. 


If  WO  substitute  in  (7)  for  B  is  apin'oxlmato  value  -. — -,  and  foi*  SB,  and  <5ai'  the 

SHI  11 

values  derived  from  the  equations  (8)  and  (9),  the  expressions  for  Sx  and  Sy  reduce  to 


cos  («  —  <»')  _,      8in(M  — oj')  ,.      r  sin  oj'  „„ 

^^  Bin,  11  "'^*  ai»i«    II  ' 


8y: 


sin/? 

sin  (m  —  <»')  *i      ^os  («  —  a>') 
Sin  n  '        Sin  // 


sin'-'  11 


dfi. 


Y  cos  CO 


(10) 


sin"// 


rsn. 


As  already  shown,  if  wo  put  «  in  place  of  &>',  the  error  thus  introduced  will  be, 
at  its  maximum  only  about  ^  of  the  total  amount  of  the  corrections,  which  will  be 
quite  nnipnportant  in  all  cases.  If  we  suppose  the  right  ascension  and  declination  as 
well  as  the  longitude  of  the  sun  to  bo  known,  we  have 

,  .      sin  a' 

COB  (m  —  oj)  =  -: — r  > 

sin  («  —  oj)  =  cot  L  tan  <S', 

which  may  be  substituted  in  (10).     IJut,  as  k  — oj  has  necessarily  to  be  computed,  it 
may  bo  more  convenient  to  use  the  equations  unchanged. 

The  expression  (6)  for  J  contains  not  only  x  and  y,  but  their  derivatives  with 
resj)ect  to  the  time,  which  aro  multiplied  by  the  interval  t—  t.  Since  we  can  choose 
the  time  r  as  near  ns  wo  please  to  the  moment  of  passage  of  tho  shadow,  wo  may  ' 
make  the  effect  of  these  terms  as  mintite  as  we  please;  but,  owing  to  the  extreme  slow- 
ness with  which  u  —  oj  changes,  the  effect  of  ^A  and  <5y9  on  the  derivatives  of  x  and  y 
will  under  all  circumstances  be  insensible,  while  tho  minuteness  of  the  correction  to 
the  parallax  will  render  the  derivative  of  tho  last  term  of  Sx  and  of  8y  inappreciable. 

Wo  may  therefore  suppose 

„  dx      d  X 

dt~'dt  ~   ' 

We  have  next  to  investigate  the  changes  which  may  bo  produced  in  ^  and  ?}  by 
changes  in  the  relative  position-s  of  the  sun  and  moon.  Tho  change  in  d  will  be  very 
nearly  that  in  tho  sun's  declination,  which  can  scarcely  exceed  20"  within  historic 
times,  and  2"  within  tho  last  two  or  three  centuries.  These  changes  would  corre- 
spond respectively  to  2000  feet  and  200  feet  on  the  earth's  surfiice,  and  maj"-  therefore 
bo  neflected.  The  changes  in  ^  and  7  will  therefore  depend  upon  those  of  /i',  or  of 
the  hour-angle  of  the  lino  joining  tho  centres  of  the  sun  and  moon.  If  we  represent 
by  E  the  equation  of  time,  and  by  ^  the  local  mean  time,  tho  value  of  m'  is 

ti  —  U-[-c  sin  OJ  sec  S ; 

or  if,  for  tho  moment,  wo  represent  the  west  longitude  of  tho  point  of  observation  by 
A„  tiie  value  for  tho  assumed  time  will  bo 

/i' =  T  —  A,  —  £ -f  c  sin  OJ  sec  5.  (10) 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


n 


of  these  (luantities,  r,  the  ubHohite  time  for  which  the  coinjnitiition  ia  made,  is 
arhitrarily  assumed,  and  is  not  subject  to  correction,  tlie  actual  time  having  been  elimi- 
nated from  til*'  expression  (6)  for  J  •,  A„  the  longitude  of  the  place,  is  necessarily  sup- 
posed to  be  known;  the  error  of  7v  cannot  exceed  u  few  seconds;  its  effect  is  there- 
fore insensible  ;  while  c  is  so  small  and  well  determined  that  the  cdianges  in  the  last 
term  of  the  expression  are  insensible.  We  may  therefore  consider  f,  and  if  to  be 
unaffected  by  any  changes  in  the  lunar  and  solar  elements. 

It  appears,  then,  that  to  find  the  change  in  J  we  need  only  change  x  and  i/. 
We  therefore  obtJiin  from  (6) 

or,  for  the  differential  coeflicients,  using  equations  (lo)  and  putting  oo  for  «', 


sin  n 


(U 


IT  sm  n  I  -j- 


lU  dx 


+ 


dJ_ 

dji 


dx) 


_  X'  sin  (m  —  a>)  —  F  cos  («  —  «). 
•     AT  d^  _  -X'  cos  {u  —  aj)  -f  F  sin  («  — m) 


sin//  -r,^-= 


F  sin  go'  —  X'  cos  co' 

V  x'^-j-y-'' 


dll  ~  sin  // 
The  most  convenient  fornuihc  for  computation  will  be: 


■S) 


•90°). 


(12) 


dJ  _  sin  (m  —  (o- 
dy  sin  77 

dJ  _  cos  {u—co  —  S) 
d'fi  ~  sin  77         ■ 

dJ  _      Y  cos  {co  —  S) 

(/77~    '  '^v^  n     ■ 

In  the.se  exi)ro.ssions,  the  unit  of  J  is  tiie  earth's  o(iuatorial  radius,  and  that  of  A 
and  /?  is  the  unit  radius  of  arc.  It  will  be  rouiembeied  that  J  is  here  the  smallest 
perpendicular  distance  of  the  place  from  tlie  centre  of  the  shadow,  and  uuist  not  be 
confounded  with  the  corresponding  distance  measured  on  the  surface  of  the  earth. 

If  nothing  more  is  known  of  an  eclipse  tiian  that  it  was  total  at  a  given  place,  J 
may  have  any  value  less  than  the  radius  <if  the  shadow.  We  cannot  then  form  an 
absolute  e(puition  of  condition,  but  can  only  at  sign  two  limits  within  which  a  certain 
linear  function  of  the  corrections  'SA  and  6ft  nuist  be  contained.  The  following  for- 
mula; are  sufficiently  accurate  for  this  purpose.  Compute  the  angle  of  the  cone  of  the 
shadow  by  the  formula 

[7.66669] 


log  sin  /  zz 


r'  \i  —  in  cos  (;'  -f '')  > ' 


10- 


.75  Ap.  2 


74 


RESEARCUKS  ON  THE   MOTION  OF  THE  MOON. 


./'beiiiff  the  aiiglo  in  ([lU'Htioii,  mid  /  th«  distfineo  or  radiuH  vector  of  the  sun,  its  mean 
distance  being  unity  as  given  in  the  ephemeris.     I'ho  formula 

,        .     ,.      [7.6678] 
...  log  sni  /  =  '■' — /—^ 

r 

will  answer  for  all  practical  purposes.     Compute  also  the  distance  of  the  moon's  cen- 
tre from  the  fundamental  plane, 

,  _  cos  (x  +  c). 
sin  //    ' 


z-zi 


and  compute  the  value  of  8,  for  the  place  from  the  third  of  formula  (3).  Then  we 
have 

/ai  =  (z  — 5)  tan/  — 0.27227  sec/;  (13) 

Pj  being  the  radius  of  the  shadow.  If  now  ^„  represent  the  tabular  distance  at  which 
the  axis  of  the  shadow  passes,  as  given  by  formula  (6),  the  value  of  J^  +  ^d  must  be 
contained  between  the  limits  +  Pi  Jind  —  p,.     The  expression  for  this  function  is 

The  condition  sought  is  therefore 

We  have  now  to  introduce,  in  place  of  A  and  p,  the  mean  longitudes  of  the  sun 
and  moon  and  the  longitude  of  the  moon's  node.  Introducing  the  notation  of  the 
preceding  article,  where  we  have  put 

e,     the  moon's  mean  longitude ; 
I,     its  true  geocentric  longitude ; 

(/'),  the  motion  of  its  true  longitude  in  minutes  of  arc  in  o''.oi ;  and 
Gy     the  longitude  of  its  node  ; 
we  shall  then  have 

6\  =  6l—6L=  ^''^ 


7.90 


St  -  SL ; 


6fJ  =  sin  i  sec  /?  cos  (l—O)  (61—60) 

=  m\  i  sec /3  con  (I— 0)  (  ^^"'  6e  — SO). 

\7-90  / 

In  the  case  of  a  central  eclipse  of  the  sun,  we  may  put  .sec  /?  cos  (/ —  ^)  =:  posi- 
tive unity  when  the  ecli|)se  occurs  near  the  ascending  node,  and  negative  unity  when 
it  occurs  near  the  descending  node,  without  an  error  of  mon*  than  ;,'-  of  the  whole  co- 
efficient, and  may  take  ±  .995  as  its  mean  value.  We  may  also  suppose  sin  /  =  .090. 
The  value  of  Sfi  will  then  become 

S/3z=±.oSgs(^y  Se  —  So\ 
Substituting  these  expressions  for  <5A  and  6/i  in  the  expression  for  SJ,  we  find 


6 J  =  /    (^i  ±  .089s  l^f ")  Se  =F  .0895  ' 
7-90  \d\  (I ft)  (' 


%">  +  %'"- n"-    (■*) 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  JfJ 

in  which  the  tUflFerontial  coefficients  are  to  bo  taken  from  (12).  This  equation  f^ixcs 
the  condition  which  must  he  fulfilled  by  the  corrections  to  t\w  elonicnt.s  in  order  that 
the  path  of  the  shadow  may  1)0  thrown  to  the  north  by  the  quantity  <'^J. 

The  upper  sign  is  to  bo  used  when  the  eclipse  occurs  at  the  ascending,  the  lower 
when  it  occurs  at  the  descendinff  node. 

In  this  ff)nnula,  wo  tacitly  suppose  the  error  of  tlie  moon's  true  lon<ritudo  to  arise 
only  from  that  of  its  mean  lonfritude,  and  nc'^'lect  the  ert'cct  of  ])ossible  errors  of  the 
eccentricity  and  periji^ee.  In  practice,  the  datum  which  we  are  considcriuf,''  will  ])e 
used  only  to  determine  the  correction  to  the  longitude  of  the  node;  but  to  dn  this,  the 
correction  to  the  true  longitude  must  be  supposed  known.  The  mode  of  expressing 
this  nni.st  depend  on  circumstances,  and  that  which  we  now  adopt  is  that  to  be  tised 
for  tlie  older  eclipses. 

§8. 
OBSERVATIONS  OF  BULL[ALDUS  AND  (lASSKNDUS. 

The  authorities  for  these  observations  are  the  printed  works  of  the  authors, 
namely: — 

Bui.LiALDUS,  Astronomiii  Philolaica.     Paris,  1645. 

Gassendi'S,  Opera,  Toiu",  IV,  Commvtitnrii  <h'  Rebus  Coelcstibtis. 

I  believe  we  must  accord  to  Hdi.LiAi.ors  the  honor  of  being  the  first  to  actually 
observe  the  time  of  an  occultation  with  a  telescope.  We  begin  with  his  observations. 
The  times  have  been  dedu(;(>d  from  the  observed  altitudes,  using  the  mean  places  of 
the  stars  given  on  the  next  two  pages.  The  geographical  positions  of  tiie  ])laces  of 
observation  of  the  two  observers  have  been  adopted  as  follows: — 


Long,  from  ' 
Latin  Name,  j  Modern  Name.   Latitude.  |  Qf„„n\vich     '°^  ''  '""  ^   '  '°^  ''  '^°^  '  ' 


Paris.     . 
Loudon  . 


Juliodunum 

Lridununi 

Dinia      .      .  .  Digne 

Aqua:  Sexlln:     Aix    . 


48  5» 

47  « 

44  5 

43  3* 


s 
21  E. 

20  E. 


24     57  E. 
21    47  E. 


9.8747 

9.S622 

9.8403 
9.8358 


q.8192 

0-8344 

9.8570 
9.8610 


It  will  !)«>  remembered  that  in  making  these  observations  the  observers  used  no 
clock,  but  determined  their  time  by  ob.serving  the  altitude  of  some  well-determined 
object  at  the  moment  of  the  phenomenon.  The  star-positions  used  in  reducing  the 
observed  altitudes  of  all  the  observers  whose  work  is  discussed  in  the  following  sec- 
tions are  shown  in  the  following  table.  No  refinement  has  been  aimed  at  in  their 
derivation,  nor  have  the  j)laces  been  corrected  for  nutation  and  aberration.  All  the 
corrections  which  should  be  apitlied  are  completely  nuisked  by  the  probable  errors 
of  the  observed  altitudes. 


76 


RESEARC'lES  ON  THE  MOTION  OF  THE  MOON. 

Approximate  Posilions  of  Stan  for  Clock-error,  carried  back  from  the  Positions  ofh^  Verrikk. 

(Ammles,  ii,  p.  [63],) 


n 

ANt)ROMED.«. 

Ycir. 

Right 

Ascension.       Dec 

i 

linalion. 

// 

m 

1         , 

■ 

1650 

23 

50 

25.48     +  =7 

y.5 

171K) 

52 

58.11 

36,0 

1750 

55 

31.17 

48.5 

1800 

23 

53 

4.66  '       27 

5').  I 

1850 

0 

0 

38.58         28 

157 

iqOO 

0 

3 

12. 03     +28 

32-3 

Year. 


1650 
1700 
1750 
'  1800 
i  1850 
iq/oo 


1600 
1650 
1700 
1750 
1800 
1850 
1900 


1650 
1700 
1750 
1800 
1850 
I  goo 


1600 
1650 
1700 
1750 
1800 
1850 
1900 


1600 
1650 
1700 

1750 
1800 
1S50 
igoo 


1650 
1700 

1750 
iSoo 
1850 
1900 


11  Akietis. 
h     m         .t 

I     44  4023 

47  35->3 

50  21.51 

53  9.40 
55  55.78 

1  58  4365 

2  I  32.02 

II  Ceti. 

h     m         s 

2     44       3-' 

46  38-7 

49  I4.S 

51  50.4 

54  26.5 
2     57       »'9 


+  21 
21 


+  22 


46.7 
37-7 
22.7 

1.7 
34.8 

1.9  i 
23.1  i 


+    3 


40.9 
53-3 
5.f> 
17.8 
29.9 
4t.3 


Aldebaran. 


4.17 
54.61 

45-32 
36.31 

27-57 
19. II 
10.92 


+  >5 


15 
16 

-I-  16 


37 
44 

52 
58 
5 
12 
18 


37.4 

54-0 

l.o 

55-7 
39.0 
10.9 
31-4 


CAPEI.1.A. 


18.16  ! 

56.94  ! 
36.21  { 

•5-97  I 
56.22  j 
3'i-97  I 
18.20  I 


+  45 


■45 


29.8 
34.3 
38-6 
42.7 
46.6 
50.3 
53.8 


/J  Orionis. 


450 

8.5 

32.1 

55-9 
19.8 
43-8 


SiRIITS. 


Right  Ascension. 


1650 
1700 
1750 
1800 
1850 
1900 


1600 
1650 
1700 
1750 
1800 
1850 
1900 


1600 
1650 
1700 
1750 
1800 
1850 
1900 


1600 
1650 
1700 

1750 
1800 
1850 
igoo 


1650 
1700 

1750 
1800 
1850 
19UO 


43-a 
555 

7.8 
act 
32.4 
44.7 


Declination. 


-  16 


-  16 


IV.I 
20.2 
23.5 
27.1 
30.8 
34.7 


'I  Orionis. 

/(       III  s  I 


36 
38 

41 

44 
47 
49 


I 

4 

7 

10 

13 

16 
19 


14.57 
56.59 
38.69 
20.86 

3. II 

45-43 

/(  Tauri. 

J 

5. II 
13-38 
21.88 
30.61 
39-57 
48.77 
58.19 


t-  7 


>7  7 

18  44 

20  10 

21  24 
32  27 
23  18 


26 


+  28 


I'ROCYON. 


19.00 
56-75 
34-41  I 
11-97 
49-44 
26.81  I 
4-09  I 

Pol.I.UX. 

J 

43.08 
48.62 

53.86 

58.81 

3.46 

7.8. 
11.87 

Rii;ui.iis. 


+  5 


+  28 


38 


10  51 

14  50 

18  35 

22  7 

25  25 

28  30 

31  21 


10  50 

4  18 

57  35 

50  41 

43  36 

36  30 

a8  53 


54  42 

4'*  47 

42  39 

36  19 

29  46 


9 
10 
10 


lit 

s 

^ 

49 

.19.78 

+  "3 

52 

20.91 

55 

1.77 

13 

57 

42.37 

13 

0 

22.70 

3 

2.77 

■+-  12 

23 
16 

I 
3 

39 

1-9 

24 

53.8  1 

10 

39.6  ■ 

56 

19-4 

41 

53-2 

27 

31.3 

RESEARCHES  ON  THE  MOTION  OF  TflE  MOON. 
Approximatt  Ppsitions  of  Stars  for  Clock-trror,  (Sf*-.— C'<intinuf(l. 


77 


/?  Lkonis. 


Year.    RiRhi  Ascension. 


1600 
1650 
r7oo 
1750 
1800 
l8so 
igoo 


1600 
1650 
1700 
1750 
I  Sou 
1850 
1900 


1650 
1700 
1750 
1800 
i8so 
1900 


i6jo 

1700 

l7$o' 

1800 

iSjo 

1900 


38 
3' 
33 
36 

39 
|i 
•)3 


a  Ly«A. 


Declination.     !'    Year.    RIrIiI  Asrcnslcm,'      Declination. 


35.  "7  !  +  >'> 
9.40 


43-43 

17. as  I 
50.87 

24. 28 

57-49 

Sl-ICA. 


h 
13 


13 

I, 
13 
14 


14 


4 

6 

<J 
12 
14 
■7 
'<J 


14.03 

50.24 
26.72 
3-47 
40,49  j       10 
"7-77  I 
55-33  '-  "o 


16 
15 


+  15 


-    9 


48 
3< 
■  4 
58 
4' 
24 
7 


2 
|3 
34 
50 

6 
33 
38 


')-7 
39.1 
47.6 

5-1 

21.7 
37-3 

;3.o 


46.0 
51.7 

53.7 

5>  ') 
46.4 

37.1 
24.1 


ARCTURI'S. 


43-0 
59-5 
16.0 
32.6 
49.3 
5-9 


+  21 

20 


2U 
+   19 


1-7 
45-7 
29.7 
13.8 
57-9 
42.2 


1650 
1700 
1750 
1800 
1850 
1900 


1650 
1700 
1750 
1800 
1850 
I9CX) 


1650 
1700     I 
1750     i 
l3oo 
1850 
KJOO 


h 
18 


5.8 

47-a 
38.6 
10. 1 

51.6 
33-2 


+  38 


38 


39.5 
31.7 
34-0 

36.3 
39.8 
41.4 


a  Aqcti.H. 


19 


19 


h 
20 


41.91 
8.44 

34.94 
1.4" 

27-S3 

54.22 

n  CyGNI. 


+     7 


31.00 
13.95 
54.96 
37-02 
19.14 
1.3" 


H-  44 


44 


59-2 
6.4 
"3-7 
31.11 
38.6 
36.3 


3-4 
13.6 

23-9 
34-3 
44.8 
554 


a  COROS.T.  BOKEALIS. 

1 

a 

Pegasi. 

h      m 

/ 

. 

/; 

m 

^    ' 

- 

■ 

15     19 

53-1 

,  +  27 

55-6 

1650 

22 

47 

22. 06 

+ 

13 

20.0 

31 

51.8 

t 

44.9 

1700 

41) 

50.74 

35-9 

34 

6.6 

34.3 

1750 

53 

19-54 

13 

M.9 

2() 

13-4 

23.7 

1800 

54 

48.47 

14 

7-9 

28 

30.3 

13-4 

1850 

57 

17.52 

24.0 

«5     3" 

27.2 

i 

3.. 

1900 

22 

59 

46.70 

+ 

14 

40.1 



Observations  of  Bulijaldvs. 

From  Anlionomia  I'hilolmiu,  p.  159. 
Anno  162.}  .lulij  ilie  5  cum  Liintie  centrum  iiitum  eswr  g.  lyj  I'aiiaiis  obaervnvi  occiiltationtMii 
SpicHC  VirginiN  a  3> . 

BiJLt.lAi.Di?.s  adds  that  the  moon  appcnrcd  13'  north  of  tlit>  star  in  latituth^ ;  and 
having  thence  compnted  its  position,  \u'  achls:— "fuit  Honi  Parisiis  ox  altitndiiio  Spicau 
p.  17.7'.  post  nieridiurn  ix.  30'."  There  is  then-fore  some  doubt  whether  the  actual 
observation  of  altitude  was  made  on  the  moon  or  on  Spiea.  The  corresi)ondeni'e 
between  the  dirtereiico  of  altitmles  and  diHercncf  of  latitude  is  somewhat  susi)icions. 
The  apparent  places  of  the  two  objects  are,  as  a  first  approximation : — 
Hpica,  A.  H.  =  13"  5™  27';  1^««'-  --9°  10'. 
Moou,  A.  li.  -  13'  4"'  40';     l^ec.  =  -  8°  46'. 


f$  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

The  jilftco  ot'tlio  moon  is  tlint  roinpnted  tVoni  IIanmkn'h  'ruldoH  fi»i'  9''  33™  37*  I'uriH 
tinu',  1111(1  coiTi'C.tod  for  piinilliix. 

TIio  local  tiiiK'H  tlieiici'  (Icdiicctl  niv: — 

From  alt.  of  Sjiini,  i;''     7',  t5id.  '1',=  16"  27'"  15";  M.  T.  =  9''  33'"  >8". 
-Moon,  17°  ao'  16"  26"' 58';  9"  SS"     I". 

Tlic  ivsnlts  ajiTco  well  enough,  Imt  the  fact  is  that  at  thin  time  the  tables,  which  can- 
not he  ,^'  in  error,  show  the  ii|)]iarent  distance  of  the  ceiitn*  of  tlu^  moon  and  .Spicii  at 
this  time  to  have  been  aliout  2S',  so  that  the  star  must  liav«f  he<'ii  Home  13'  distant 
from  the  moon's  dnik  liiid).  'I'he  moon  was  then  a  few  hours  past  her  first  (Hiartor. 
Moreover,  the  moon  was  about  20'  north  of  tlm  star  in  latitiule,  so  that  there  could 
not  have  been  an  occiiltation  at  all.  Indeed,  a  careful  readinj;"  of  Hii,!,iaM)Ih's  dodnc- 
tioiis  from  his  observation  seems  to  indicate  that  he  considered  the  two  bodies  to  have 
the  same  loiifiitiide  at  the  moment  of  the  ohservntion.  Now,  we  must  adopt  0110  horn 
of  this  dilennna:  either  (i)  wo  have  to  deiil  with  sn»di  u  blnnderin}i'  ol)Mervor  thiit  ho 
thonyht  ii  star  at  the  moon's  liinli  when  it  was  23'  distant,  and  in  foiijnnction  when 
the  dillficnce  of  htngitiide  was  some  20',  and  that  when  the  ditdiotomi/.ed  position  of 
the  moon  was  most  favorable  to  the  observation;  or  (2)  he  made  11  mistake  in  readin<j 
his  altitude  from  the  quadrant,  and  a  conseciuent  error  of  some  40'"  in  his  computed 
time.     The  latter  seems  likely  to  be  the  correct  explanation. 

fxASsKMHiH  at  hijiiie  was  more  successful.  At  the  time  when  tlu;  altitude  of 
Spica  was  10^  46'  (local  mean  time,  10''  32'"  40"),  he  say«  Spica  was  in  the  same  ri<rht 
line  with  the  cusps  of  the  moon,  the  space  bein<r  apparently  equal  to  the  diameter  of 
Arctunis.  This  was  45'"  in  absolute  time  later  than  the  tdiservation  of  lhL.,iALi)rs. 
On  the  whole,  we  can  (h»  nothing-  with  this  (d)servation. 

The  next  occultatioii  is  oueof  a  Leonia,  1627,  June  1 7,  and  is  quoted  by  (jIassendi's 
as  fidlows  :— 

KaniloiiiOccultatioiK'in  Isaiacl  lialliiihlasotmervavit  IjO(luiii((|Uo<l  oppidiiin  I'ictiiiii<)cst<lirt'Ct6 
in  Horcioii  ac  distat  »b  eo  iiMicis  iisaalilius  10  sfa  (icriniuiifis  6|j)  horn  9  niiii  ^^  (-'H"'  laeaipo  i  u 
vcrticK  I'ori't  73  ftrad.  32  iniii.     Nota  Pohirem  clevtitioiUMii  ilh'ic  esse  48°  i'. 

From  the  description,  this  place  must  be  Loudon,  the  latitude  assigned  being  i^ 
in  error.     It  .should  be  47°  i'. 
The  altitude  gives: — 

Local  mean  time  of  occiiltation g^  29"'  42" 

Greenwich  mean  time g*"  29"*  22". 

Viiiiv  i.i.;. — Anno  1634.  Julioiluiii  a]>nil  I'i(;toiit's  cniu.-'  Meridiinnis  riMMovctiir  a  I'arisiciisi 
o('casnin  vt-rsas,  (|ihi(hMiitn  IVrnii'  lioiac  unius, oljserViVviowinltatioaiMa  iin^uli  oriiMiliilis  qaailrilatcri 
I'lt'iiiilnni  i|n;M- iK:  lucida  IMciadnin  ili(;itiu' interveata  Lanae  t'^ictain  l)cc«-rnl)i'is  die  30  ia  distaiitin 
(K-nIi  Tanri  a  vcrticc  p.  57.  icS'.     IIoi-.  5.  42'  vi'sperc. 

The  position  of  Louiloii  is  <f/ =.  47"  1';  A  no'"  20" east  from  Greenwich  The 
position  of  «  Tauri  was  H.  A.  =  4''  15'"  3";   Dec.  =:  +  '5^  43'-     ^V^'  hence  find: — 

Hour-angle — 3''  54'"  30" 

Sidereal  time o''  20"'  i;}' 

Local  mean  time S*"  44"'    4" 

Greenwich  mean  time "''  43™  44". 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


79 


VtxHf  ifi6.— Anno  »6.^9.  A|iiillH  die  7.  in  iiltiliitliiif  rroc.voniH  a.  ■^^.  <:,•.'  I'misiiN,  id  cut  llor. 
9.  8.'  T.  A.  rniiiil)iirKi  H.  9-  5^>'  '''■  A.  iit  inctlio  II.  9.  54.'  viili  l.iiiiiini  linilio  (iltsciiio  imciiIIiik*  Htcl- 
lain  <|uiiita«  Mii)({iiitiMliiiiH,  <|iiMi'  «>st  in  oii^'iiii*  citiiiii  llorciilis  'runii. 

The  roHiilt  of  tin*  ultitndr  of  I'rocyon  is;  — 

liociil  mean  timn 9''    <)'"  42" 

liuciil  Hidcn-iil  time 10''  13""  13* 

(iruoiiwic'li  iiioaii  tinio , 9''    o'"  21*. 

Tho  Htar  ti(Tiilt«'il  in  r'l'iiiiri. 


I'h|Iu  167. — AiiiKi  1641.  A|iiiliH  (lie  13  aitu  VfrMnn  occmihiiiii  IlnriitTo  Dcxtni  OtioiiiM  );.  34  o'. 
Ilor.  8.  8'  I'aiiHiiH,  l.inia  iiiilii  (ircultavit  ociiluin  llonniiii  S.    (liociis  Tyirlidti  U  t;.  j.  >'7'') 

Tho  roHuhiiij,''  hu-al  tiincH  arc: — 

Sideri'al 9'' 42'"  7' 

.M(!au 8''  13'"  4'. 

The  oce'ulted  Mnr  i'«  e  Tauri. 

Tklipsca  nnd  ncciiltations  ohservril  bi/  (tAstsENnuH. 

1631.  MvUHe  Maio,  Die  20.  (Men  nt  vul[(ii(«  laiinurat,  die  21.  Man*-)  Kclipsin  HoliH  liaiu;  obHorva- 
bam  A<|iiiH-8(<xtiiH.  ModiiH  aiitcin  Obwrvatioiiis  f'liit  buiiisiiitMli.  TiiilicicliMiitiii'  liudil  Solati's  In 
(titauM'ain  lit  it  ()<■*■]  nsani  ikt  probatnui  Telcncopiiiiii  t'oraiiiiiii  idoiu'o  in  Mii|irt'iiia  t'lMicHtra  a|i|iiii'atniii 
ft  f'ulorond  iiiotUH  |>i>,sitnM|nt<  varioH  arvoininiHlato  impositiiin. 

AdtM'at  il)i  (itMiiiatiim  iihmim,  qui  IVIi'Hcopiuiii  iiiotitaiido, eiict'  min  liicis  in  roncavo, sen  infcrioro 
vitro  appariMili'in  continno  irstitncret,  dcstincrt'tcpic  in  int-dio. 

KxL'ipicbani  vffn  Haiiios  atViM'tu  piano  solido,  pap.vro  Candida  ol)du('t(i.  Diixci.ini  in  co  ('IicM' 
lain,  in  tpicni  radii  c()(;crenlnr,  tit  in  cilipsin  nun  cxcnrrcicnt.  Diainctinni  pcdc  I'ariMicn.si  ali- 
(piiinto  inajoi'cin  diviHcram  in  partciH  acqnali'iM,  sen  Di^itos  12.  i*^  ipicinlilii't  Dij^itnni  ila  Hubi'iis- 
tinxcrani  in  dciuiH  &  qiiinaM  partcis,  nt  liucrct  ctiaiii  sin(;nla  iniinita  per  Into hI ilia  colli^'cic. 

UtraiiKjiic  ctiani  Ncnii'Cir<;niii(ercntiain  in  180.  parties  'lisnibncniin  (initio  ntrinsijnc  divisionis 
facto  al>  ipsa  Kadicc  priini  di^^iti.)  tnni  nt  in  nni^iia  occidlationo  liccrct  si-inpcr,  usnrpata  liciiu^ 
iiidc  acqnuli  ail  iiiterl'cctionct*  ('irciilorani  Incis,  \-  nnihrac  tlistantia,  cop'ic  radios  in  Circninni  iV 
iiiinorcin  inaxiinnin  iiinbrao  in  Dianictrnai  rcjiccre;  tnni  nt  exindc  Dianictrtu'nni  ntrinsijac  asiri 
appariMitiiitn  liabcri  poxsct  inntna  proportio. 

Adcralpracdictn.s  Galtcrins  in  proxinia  Caaiuni,  aHsidne  scctatns  SSoliHaltitndincni  (jnadrantc 
Kadii  pliistpiaiii  bipcdalis.  Erat  vero  penes  iiie,  ipii  statini  ati|ue  apparcrct  oliscnraiioniH  ves- 
tijiiain,  iciii  parieti  iinpacto,  inoineiilnni  ipsi  si;;nitiraret.  tjinirc  iioi;  si^nui  iit'tavit  praecise  Solis 
allitiidiiiHin  initio  KclipseoM;  iie<|ne  ratiiuie  alisiniili  cainlein  accnrate  accepit  in  line,  sen  (pio 
iiioinento  obscnratio  ex  circnlo  prorsiis  evannit. 

OinniliaH  ei'p>  appiiine  instrnetis,  oliseivatnri  adfaiiiins  al>  liora  circiter  6.  ita  scilicet  vere- 
bainnr,  lie  rallentecalcnio  initinin  praeteriaberctnr.  (Jiinnpie©  tempore  Kelipseossnpponatnr  Inisso 
in  o.  j{rnd.  15.  iniii.  [I  apparvit  nobis  praedic'a  die  20.  Kctiipseos.  Initinni  bora  19.  min.  5.  sec.  28. 
ele\rtto  neiiipe  0  25.  ^rad.  30.  min. 

Finis  liora  21.  min.  31.  sec.  12.  elevato  s<'ilicet  ©  51.  {{'"''•  '7-  '"'"• 

Ac;  medinin  proinde  coiitifrit  bora  20.  min.  18.  sec.  20. 

Et  teinpiiM  inciileiitia"  tuit  bora  1.  iniu.  12.  sec.  52. 

Et  tota  diiratio  borarnin  2.  mill.  25.  sec.  14. 

Di(;iti  ecliptic!  iiiaxiinae  ob^enrationis  fnernnt  9.  min.  2^, 

Et  qnia  tuni  deticicbant  utriinqne  ex  circiinifereiitia  ((radim  77.  min.  30.  liiniic  aeqnalos  visau 
nrguuiitnr  Liiininarinni  Diametri. 

Fuit  LuDH  Soli  SupteiitrioMuliR;  quod  circuloH  tiobiH  citra  telescopiiiin  tenierari  caoperit  ail 
Austrum. 


8o 


RF.SF.ARCIirS  ON  THE  MOTION  OF  THE  MOON. 


FiiitCoi'liiin  iiitt'rs|H'iHiim  toliim  toiiiport^  Kdipsi'os  niriorihimnubiliH.  .Iiivalmiil  illii  ntOpoK- 
Hut  Roiispici  ociilo  It'll'  iiK'OMiiivt'iiti,  i*t  spi'('illo<|iii(UMii  inaxi.iiit'.  (Jonspci'tus  vt'io  ♦'8t  t'tiiiiii  iiiiioxit- 
tiiiii  in  spt'ciilo,  Iniri  in  :i'|ua  iiinpiilii;  cum  ntntbiquo  tics  vl('erentur  i-xliitieri  Sol^s,  i|UH8i  trw 
Lniiii*'  coi-nicnlatjii'  ex  oi'ilinu  posiliic,  vorMin  ooriiiliiiH  ail  <>i;rasiini. 


Ik?  iiltitudos  yiv(! 


I.ik'mI  ini'iin  time  of  huiiiiiiiiiiij- 


jgi,     ,...  ^--.   ,,f,>,„i^  21''  27'"  17" 


(iri'iMiwicli  iin'iin  time  of  Iteffiniiiiii;'  .      18'' 39'"  50";  ofiiiiil,  21''     5'"  30". 

1627.  MciiMo  .liuiio,  I)ii'  17.  Vespori,  luinc  (MsoiilliitioMiMn  CiirilJH  Leoiiis  i\  Lunn  observabani 
Dinliie,  ciini  siMlicct  t'invt  (.'aiida  .vl  altu  ail  Ud'aKiun  25.  urtul.  13.  uiln.  hoc  mt,  hunt  10.  luiii.  30. 
praor.is)' (iitol)ai'  ilicto  iaiu  antt' (juadrato,  cuius  umbra  ivcta,  scu  tant;(Mi8  oxliibiiit  parteis  4710) 
Luna,  liiin  corniciilata  lirnbo  huo  OrliMitali,  hi'II  parte  oliscura  Cui'.  ^\\,  subiit. 

I'Diiii  tiiiii  U'ctura  trii'iito  A  cDrnu  inti'riori;  tandem  veri)  texit.  iioii  xiidlo  anipliiis  i|nndrante. 

Observatii  est  autum  non  niido  suh'ini  visii,  (|Uo  Stella  videbiUur  Luiiain,  quasi  adreperido, 
radere;  viM'iim  etian)  pitr  Telescopiiitn,  quo  distnntiola  qiiaeiiuu  ad  iieeultationoin  usque  diHtini;!!") 
percepta  est. 

TIio  iiltitiidi'  of  ft  Leoiiis  <(ive8: — 

Loral  nioMii  tiiiu>  of  oc'cultation 10'' 30'"   o' 

(irt'C'iiwirli  iiicau  timo 10''     5'"    3". 

1630.  Caeterum  eopiain  s\  Sebiekardo  iiostro  tibi  iaui  oxistimo  factani  niuae  illius  observationis 
oirca  Kelipsin  Solis  nuperani  diei  10.  Juiiii. 

I'age  545  — Nisi  luerit,  seito  nobis  in  hac  Civitato  (cujiis  latituilo  est  48.  t;i'iid.  52.  inin.)  illiiis 
initiuu!  I'untiKissc  Soleadnceasuni  altof^rad.  14.  min.  40.  sen  liora  p<l^4t  meridiem  6.  inin.  i6>j,  Fiueni 
videre  non  potuisse,  proper  Holis  oeeubitiim,  ciiui  dnonim  prope  diKitorum  foret  adiiui;  obseuritaB. 
Medium,  ipiateiius  licuit,  observatum  pruxime  fuisse  Sole  adliuc  eluvato  grad.  6.  min.  30.  seu  bora 
t'irciter  7.  nnn.  12. 


Tlio  pluco  of  observation  was  Paris      Tlie  altitude  {jfivcs ; 


I..ocal  moan  tiiiio  of  l)i'fiiiiiiiii<f     .     . 
(irt'L'iiwicli  mean  time  of  iM'jrinninjf 


. I  line  10,  6''  15" 


I' 
,^ j^ Inne  10,  6''    5'"  40". 

I'i'K*'  .St  7- — '632.  Febri'arii,die  5. — Credebani  L'tiani  facile  tore,ut  )..unadunta.\at  Mart  em  sirin- 
Kcret:  nisi  ipiiid  ad  coiistiditionem  I'oli  Kelipticae  respiciens,  non  ouuiino  ilesperabani,  qiiin  vul 
tantillum  oeisdtaret.  Nee  vern  tan.i  I'liit  spes.  Siquidem  iam  sub  lior.  3.  ciirn  plurimuni  illi  quasi 
ailrep.'iisset,  ac  Mars  jiroxime  accessisset  ad  vertie:  lis  liUnae  planiini,  turn  demiiin  Luna  i\Lirtem 
oeculuit.  OontiKit  ista  oecultatio,  cum  liinbns  j||-ir  Lunae  supremiis  I'oret  altiis  ad  ocea.sum  (j^rad. 
14.  min.  17.  iS:  eodeni  tempore  .Vrctiirus  (oret  altus  ad  exortuiii  )j;rad.  ~,ft.  min.  10.  Kxpe(;tati> 
postea  e^ri'ssu,  etsi  vapores  iam  I'uerant  loi'^e  iimplins  deiiHiiu'es  tacli,  varieKataqiie  irradiittio 
('ileum  Luiniiii  dittundebatur ;  apparvit  tamen  cmer^'ens  In  miilta  iam  niclinalione  ultra  planum 
verticalis,  cum  idem  limbus  Lunae  supreuius  esset  alius  ad  ocu.isum  gr.  39.  min.  57.  eodem({UC 
inoniento  ad  ortom  I'oret  Lneida  Lyrae  nita  ^nu\.  31.  inin.  54. 

The  oltservtUivMii'i  f;ivo: — 

Immersion,  fnmi  altitude  of  .\ntunis,  Loral  M.  T.  15''  18™  39";  G.  M.  T.  is"    9"'  iS'. 
Kmorsion,  from  altitude  of  «  Lwii;        Local  .M.  T.  15"  47'"  31";  G.  M.  T.  15"  38'"  10". 


RESEARCHES  ON  TIM.  MUTIUN  UK  THE  MOON, 
Edipse  oj  1633,  April  8,  o/wnvil  tit  Dignf. 


Sr 


PhBHUH 

Kcli|>Hir(is. 


I. 
2. 

3- 
4. 
5- 
6. 
7- 
8. 

lu. 
II. 
u. 
>3. 
'4- 
15- 
16. 

»7- 
18. 
!(}. 
20. 
21. 
22. 

n- 

as. 

36. 
»7- 


V*i>aiilitu8 
OvfuctiiN 

Gndui 

lilnc  inUe 
(Itticiciitcs 

dig.     m. 

Rr.  Ill 

4.     30. 

5". 

5.      42. 

f8. 

7.       0. 

65. 

7       30- 

68. 

8.       6. 

70. 

8.      12. 

7>- 

8.     18. 

7a. 

8.     18. 

73- 

8.      6. 

70. 

7      4a- 

68. 

7.     30- 

('!■ 

7.     12. 

65. 

6.     48. 

Oj. 

6.     36. 

62. 

6.      12, 

60. 

S.     30- 

55. 

5.     18. 

53- 

5.      0. 

sa. 

4.     30. 

50. 

4.     18. 

48. 

3-     42. 

45- 

3.       0. 

39- 

2.    4a. 

w. 

2.      0. 

35. 

1.    36. 

30. 

0.    54. 

30. 

Finii. 

0. 

rimtluft  incH- 

nallii.      L>la- 
nicir.iTuiii  uil 

Alt.    .,  In 
luirtibiis 

I.UM. 

Veiilc. 

V.      R 

Kf       111. 

32. 

3S. 

50. 
62. 

72 
85. 

107. 

112. 

:i7. 

122. 

125 

12a. 

132. 

"34. 

136. 

138. 

140. 

141. 

142 

143 

145- 

147- 

14? 

150. 


S«u  rcft|>cctu 
habllu  tinii 
rclr  tiitii 
paralUxcuH  I 

Kratl.    mill. 


5150. 

4050. 
3950. 
3800. 
3720. 
354')- 
3150. 
33<x>. 
3030. 
2(>20. 
2850. 
2800. 
2750, 
3670. 
2560. 
2450. 
2350. 
2260. 
2230. 
2160. 
2060. 
2ono. 

Il/K). 

.74"- 
'.(*yt. 
1430, 


35.   15. 


20. 

20. 

"). 

•')• 

18. 

IC. 

16. 

I5' 

15- 

Ij 

14. 

14 

13. 

13 

12. 

12. 

12. 

II. 

II. 

10 


3 
33 

48 
a4 

30. 

2.  I 

16,  i 

"•I 
"7-  I 

54-  i 

3<), 

S3,  i 

"•  I 
23.  ' 

46.  ' 

13. 

44- 

34 

II. 

38. 

I.J. 

45, 

■2. 

5- 

S'  i 


37.   13. 


23. 
21. 

20. 
I   20. 


I'l 
18. 
18. 
16. 
if.. 
IS- 
IS- 

15 
14 
I» 

13 

12. 
12 
12. 
II. 
II. 


o. 
2iy. 
43- 
19. 
as. 
56. 

<)■ 
41 

'J- 
4'' 
3' 
15 
48. 
13 
37 

4- 
35- 
35 

I. 
23. 

'(■ 
31 
41 
m. 
53. 


Hro|«>rllo  Dia- ; 
liiL-tri  C  ad  ' 
Diaiiiutr.  ^.t 
Sit  v>.  Sum.  ' 
15.  m  2«.  HCI-.  ; 
A  Sviii  <  I 
mill.       sec.    , 


3. 

56. 

3. 

0. 

26. 

H. 

2.,. 

8. 

.33i. 

I-J. 

36. 

IS- 

41. 

13. 

431- 

7- 

48. 

I7». 

5"- 

15- 

5')- 

M  . 

I. 

17. 

'■ 

7- 

S- 

4. 

12. 

7 

10. 

, 

10, 

13. 

5' 

13 

'5- 

16. 

10. 

-■ 

"'< 

2. 

, 

30. 

5 

22 

6. 

25 

2. 

27- 

2. 

30. 

1 1. 

52. 

*• 

35. 

"*' 

t^ 

'>3J- 

10. 

45- 

• 

Tlio  rosiilts  ;»f  flu!  (ihstM'Vfitiitii.s  will  he  yivou  in  (lisciissiii(>'  the  eclipses. 

1635.  .\HK.  26. — Occult  alio  iiriu'ri'dciilis  iliianiiii  Caiidiii'  '}  a  ([.iinia  IvcpK'iiis  iiioiiiu'rat  loiv 
lit  d  Stt'lliis  Cttiidat'  >  tt'fjcri't  iiolii.s,  idcirci)  atttMidoiidiiin  dii.\i  ipiid  liae  do  re  (•()iitiii;;i'ii't.  VA 
iiiiIk'h  quident  puroxigiiain  relJi|iiL>rniit  .spcin  qiiiuqiiain  obHorviuidi,  ac  ])otisMiiiMim  cin-ii  pnu'ccdi'ii- 
ti'iii  diianini  }-  in  taiitii  ([  viciiiia,  ob  illiiis  oxilit.tttMii ;  vi'ii'iiii  tainctNi  iili.stilciuiit,  i|ii(i  iiiiiiiis 
ii'licta  i\  d  deti'ffi  iisi|uaiii  potiirrit,  |H'riiii.«<i'ri.>  taiiicii  ip.siii.sciinsiu'ctiiiii,  ciiio  inoint'titi)  olilc},'!  (-(u'pif. 
Viiric,  iic  noil  sine  laltoro  st'ctatii.s  illaiii  fiu'raiii  ctiaiii  in  iNlinoTclc.si.iipin,  oli  imivi'isi  |iiiipi.|iiiidiiiii 
iii'iiH  inibilo.sitattMii ;  soil  ravtirc  cvimio  di.stiiicli.ssiiiio  vi.sa  est  :^  .scn.siliili  iiittT.stilio,  i|ii<iii.><i|ii('  pai'iii- 
contiKiia  I'liit  illiistnito  iiiar);iiii  oriiMituli  <[  iillia  ipioin  (adiiiic  aspfialiiiii)  taiitiMiiiii  siiptMcrat 
iiiarjfiiiis  illius  obscnri,  piaotiT  qiu'in  I'aota  ttiiKU'iii  est. 

Liiiiii  itaqito  snbiit  Htelhiin  (■  ri>(;iotiu  siipciitiii.s  paili.s  Mauiilau  );>'i><>ilii>^>'*'l:tt'i '■'^ '^'■'lOi^t^-'i'i-'^ 
rutiiiidai',  qiiiic  ost  ad  laevaiu  nnibilici,  hoc  «'st  infra  im-diiiin  oriciitalis  inaiKiiiis  parte  rtit'  dimdf 
ciiiia  totiiiH  aiiil>itim  LiinarJH. 

Knit  aiitfiii  tunc  liicida  V  Jam  t-Ii-vata  ad  Oiliiiii    jjv'- f'"'"  '**•  Kiad.  31.  miii.  nude  proditiir 
liora  I),  mill.  47.     l''uit  &  iiiarjji)  .superior  <i  altii.s  1910.  sen  iO.  \i\\  17.  iiiiii.  ae  pniiiulc  Htella  occiil 
tata  25.  K'wl-  57-  '»'"•  l>roxiiii(>,  iiiidc   prodiliir  bora  1;.  iiiin.  501...     Knit  deiiiqiii^  aililndii  Capitis 
Andionie<bie  9400.  sen  43.  }:rail.  14.  mill,  imde  proditiir  bora  >)  iiiiii.  50 credideriiii  lioraiii  u  iiiin    19. 
II 7.".  Af.  '-' 


82  KKSKARCHES  ON  THE  MOTION  OF  THE  MOON. 

Tluf  results  tVom  tlio  tlireo  altitudos  of  stars  are : — 

From  '5Aric'tis:  Localiucantiino,  9*"  47'"49";  lumr-aiiylo, 

Kntiu  a  Aiulroinutla-:  Local  moiuitime,  9''  52'"  25";  liour-aii<i;lo,  —  3''  39'"  29' 

From  /Capriconii:     Local  mean  time,  9''  57'"  34";  lioiir-aiifrlc,  —  i''    4'"  24' 

The  most  proliable  moan  time,  9''  50™  12". 


-ii  ,,111  - ,« 

0  jy  3j 


Oeculttifioiis  of  the  I'Iciitdvs. 


1637.  MiU't.  (lio  29.  Ai|iiis  Sexliis. — Tuiu  quia  ^  jnii  cv<uh;t>:tt  Stullsiu  iii-oiiiiii|ii<i  aihiiodiim 
iliviTtcMi;  alio  null  pluciiit.  Itaipie  Jiissus  est  Agarratiis  assidui'  so(;tai'i  altitudiuuiii  ipsias  AUIebii- 
lai'ilaia  ii)so  Tfk'S(H)pio  ad  occultationeni  attendo.    Ciutt'iiitM 

Occultatio  .Sti'llai!  aiigali  ocicidai  in  n  I'leiadam  (iontiKit)  ciiin  altitudo  Aldebarac  forct  20. 
(^r.id.  55  Miin.  iu;  proiadc  bura  S.  iiiiii.  44. 

Uicaltalio  .Stellat!  angali  IJorei  in  a  I'li-iadain  <ouli};it  cam  Abltdjaraoallitado  foiet  14.  giiid. 
50.  inin,  ae  proindc  hor,  9.  niiii.  19.  ooascMpieiiter  aut(Mn  Cait  altitado  <i  siiperiore  lanrgiiic  10.  grad. 
50.  mill.  \  liK-idae  IMeiadaiii  1 1.  j^rad.  o.  niiii.  attpie  adeo  luira      .  iniii.     . 

Oecaltatio  Stellao  aii^tali  Anstiiiii  in  a  I'leiadaiii  conti^it,  ciuii  Alili'barao  altitado  foiet  13. 
grad.  io.  mill.  \w.  proinde  lior.  9.  min.  26,  it  Sti'llac  in  i-xtiemo  conni  Itoieo  ")  29.  gra<l.  31)  iiiiii.  sou 
bora    .  mill.    .     Fait  iJt  coasfipioiiti'r  altitado  ([  9.  grad.  25.  iiiiii. 

()i'(.Miltati(i>Strllau  aiigaliortivc  in  a.stni  liicidac  rioiadiim  cuiitigit  cum  alliladuc.vtivar  coriiii 
Uorc'i  ii  I'oix't  26.  grad.  35.  aiiii.  ac  proiudc  bor.  9.  miii.  45.  fait  eoiisefpiuiiter  altitado  Aldubarac  10. 
Kiail.  JO.  mill,  mule  bora      .  min.      .  &  coiiseipu'iiter  ({  6.  grad.  50.  iiiiii. 

Tlie  altitudes  j,nvo  : —  ' 

IimiuTsion  of  Klectia;  Alt.  of  Aldebaraii:    l..ocal  lueau  time,   8'' 4.S"  58". 


Immersion  of  Maja  ;       Alt.  ttf  .Mdebaraii:   Local  mean  time,  9'' 


I 


iiiuicrsutn  o 


f  M 


M'l ! 


Alt.  of  //  Taiiri:        Local  mean  time,  9'' 


4—« 
/ 

18" 


Imiiii  Tsioii  of  ^^(•r'o|K•:  Alt.  of  Aldeliaran:  Lcx-al  mean  time,  9''  32"'     3". 

Immersion  of  .Mero[)e;  Alt.  of /y  Tatiri:  Local  mean  time,  9'' 33'"  10". 

Immersion  of //Tauri;  Alt.  oi  fi'Www'i:  Local  mean  time,  9''  49'"  41". 

immersion  of //Tauri;  Alt.  of  .\ldebaiaii:  Local  mean  tiim;,  9''  48'"  57". 

1638.  Jaiiuaiiu.  Diu  2|.— Vespuii,  appuLsu.s,  &  ocjultatio  I'leiuduui  a  c;  Uictaiidam  (piidciii 
tait  cam  vciito,  scsc  ob  iiimiam  violciiliani  qii()(|iiovcrsaiii  iiisiiiaaiitc,  itL'impio  ciiiii  co  tVigor  ',  ipio 
iiilcii.sius  iiicihiiiil  iicinii;  scd  iioii  licait  spcctacaltim  dimiltciv,  iiioli.scivatiim.  I'aiicis  itii  piu  ([ 
liaiisiit  |U'<i.\iiii('  ;iii.^iiluia  oci'.iilaam  .\  L'lciadiiia  siio  aii;;nlo  IIihco,  (miiii  distaiititi.  ipiaiila  a|  pariiit 
iiilt'i'  siipciioivia  c.jii.s  liiiibaiii  &  iiii^rcscciitom  I'ba.st'olaai,  wa  parte  diiimctri  wimaiis  ipiasi  ,'„. 
idipic  alto  pi'o.viiiif  rolliaru  ad  ortum  45.  grad.  o.  mill,  bou  est  bora  7.  min.  23. 

li  tc.vit  aiiKiiliim  Aiistiinnm  A  riciadam  parte  oli.s(aii'a,  iliai'iictricpie  suae  (jiia.si  .{.a  I'xirco  sal 
aii;{iilo,  iK'iiipc  ('■  rt'gii)ii(>  tfloliali  iliitiH  muJori.'<,  <|a('m  ('artbiisiaiii  dici'i'u  .soico,  rait  taiililliiiii  iiiforias; 
idipu'  roliaiH^  sillo  .(6.  giad.  30.  min.  boc  est  liora  7.  mill.  31. 

^  to.vit  lacidaiii  IMciadiiiii,sca  aiiKiiliim  .,  ortiaam  p.irli)  diaiactii  ipiiisi  !,.ii  lioivasiii  cas|iidt>, 
sciliet't  in  medio  saperioris  maris.  lOrat  aiitem  tunc  Liiuida  in  ore  ^'l  alta32.  grad.  15.  min.  (l*ollu\ 
<pii|ipe  ineoinmoilc  d('iiict'[».s  observabilis,  tliverijert'ipic  cogobat  voiitus)  boo  est  bora  7.  niiii.  52. 

Wo  liave  from  the  altitmles  : — 

Immersion  of  Meropo;  alt.  of  I'oHux:   Local  mean  time,  7''  39'"  34". 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  83 

Tlio  cortiiiii  iduiitillciition  of  the  otluT  star  oilers  (lini«'iilty  : — 

If  tilt!  Htiir  1)0  «  Leonis,  wo  have  lociil  moiin  time  about  g*'  30°  (too  late). 
If  the  star  bo  ^f  Lf^oiiis,  we  have  local  iiieaii  time  about  S''    4'"  27". 
if  the  starbe  A  Leonis,  we  have  local  mean  time  about  S''  22'"  20". 
If  the  star  be  f  liCouis,   wc  have  local  mean  time  about  ^''35"'  10". 

Orntlldtion  <>/  n  (i(  iiiiii'Oinii  ohsrrrrd  til  Diijur. 

i^ij.S.  I)p(!oiiil)ri.  Die  21. — l'ot(M'iuM  cinii  (t  .jiim  prorsiis  ('xucrct  hmimtmIjIc  iiiilliiin  olitnioliia- 
t'oiicin  ill  situ  piioiir  licic  (lusrrlpto.itii  prnmotit  iiilfris'i  fiiit  versus  caui  Ktclliiui^iiuiiccst  iuextrcnio 
p('(l(>  (!iist()iis,  iiiitf-coilitvi!  tiliaui  ill  pcdi-  proi'oili'iitis  1 1,  ut  iilaiii  mi'diu  siildi'i'jt,  tcrranipip  oripuiMit 
<piiii>  iii(i\  ante  ipsi  (>ripii<>i'iit  BoU'iii ;  scilicet  ipsaiii  (i(;(Miliiit  puiiln  iiifia  iiiiiei,liin  piirv  iiiii  ipiaiii  itiitio 
ill  pnrto  ({  orieiitali  descripsiuius,  ac  taiito  qiiiileiii  iiitorvalli),  ipiaiititui  iiineiil,.  lou;,'a  est :  aileii  ut 
locus  fiicrit  (|uasi  iiieilius  inter  priiiiatn  liet'ei^lioiieiu,  &  recnperatimiciii  liicis. 

I'liit  auteiii  tunc  liiiiiieriis  dexter  Oriniiis  ad  Occideiiteiu  ad'iin:  alius  _•^5.seu  15.  ;;rad.  54.  mill, 
atipie  ide.irco  exstitit  liora  I*'),  mill.  37. 

The  altitude  <;ives  : 


•W 


Local  mean  time,  16^  36'"  34";  Cireenwich  mean  time,  i^**  1  i' 

.  J-lcHpse  0/  tliv  ,Uiii  ohscrnil  at  ili.r,  idy),  •fiiiir  I. 

1639.  Muii.su  Jiniio,  Die  1.  A  iiuM'idie,  ICulipsis  0.  Fuerat  Cneluiii  vespere  toto  Diei  jo.  ob-scu- 
ruin;  a  iiieridie  vero  diei  31.  eliaui  ))luv<uin. 

Hoc  innne  variiiiii  e.\istit,a  iiieridit^  potiiiH  sereiiuin.  lii  ipso  uieridie  tainiiliis  atleiideiis  ad  0 
nititudiiietn,  doprelieiidil  illaiii  (piadrante  li^iieo  pedum  prope  Iriiiui,  ipio  usuriis  eraiii,  6.s.  jjrad.  38. 
mill,  uiide  quia  0  fuit  in  iC>.  grad.  36.  iiiiii.  IF  (•am  decliiintioue  IJ.ireas  2:-.  f;rad.  7.  iiiin.  (!()lli;;itur 
aUitiido  I'oli  43.  };rad.  36.  iiiin.  lunjor  ncfpio  triiuis,  vol  4.  iiiiiiutis.  Apparata  iiiterea  est  sceiia  in 
supremo  Solario,  iiiide  lielipsis  oliservaretur,  iiidu('ti'ir|ue  in  cam  macliina,  ipialiMii  l»ni':ie  iiiuxpie 
lialtueram  eiica  ICdipsiii  aiini  1633.  lieiiu;  par  I'uit  oliservaiidi  modus,  .sed  iioii  aecpia  lelicitas  piiipter 
iisur|)atuni  Teloseopiuui  majus,  (pioil  H|u>cietn  Solis  in  ciiciilo  trciniilaiii  niiiiis  exhilmit,  |)iopten|ue 
ipsaiii  iiuudiiiiam,  tpiae  iioii  satis  aeqiialiilis  seciiiidiiiii  oiiiiieiii  motioiiem  t'liit  I'^tl'i-etuiii  neiiipe 
exiiide  Ci-'t,  ut  tametsi  Corlieraiius  dirij^erer  macliinam,  i|)se  eiiruliiiii  teiiiperarem,  adjulaientipie 
etiaiii  viri  in  civitate  priiici|ies,  (alias  prol'eiMo  iinporttini)  in  adnotandis  partiluis  tain  i|>siiisdianietii, 
<pii\  niiilirau  l.uiiaris  inaxiuiiis  tumor  pertiiigeltat,  (iiiii  ciiriiml'ereiitiae,  (jna  lieinc  iiide  arcus  con- 
spicuuH  ciiisdem  iimluae  iiitersec.aliat ;  iiiliilominiis  species  Soils  extreinorum  luohilitate  oimiIos  saepc 
deiiisei'it  et  partiluis  liiijiismodi  iioii  satis  coiistanter  desi^iiatis,  diametrorum  propoitio  aucupaii 
potiHsiuiiiin  expetioraiii,  prodita  t'lieril  iiicdiistaiiter. 

Noil  distiuxeraiii  piu'io  diaiiu'tnnn  in  diioiienos  di^qtos,  di^itoiiimipie  miniita:  .sed  in  jtarteis 
100.  &  diiplatioiie  in  200.  at  ex  radio  siipposilo  100.  vei  aiiipliatioiie  100000.  cali'iiliis  essel  brevior 
ad  retexeiidiiin  eaiii  proiiortioiiem  ciiiii  &  rediictio  iiidi;;itos  fiitiiraesset  pertacilis.  .lam  iV  i'aiiiuiiis 
extra  scenaiii  atteiidil  coiitiiiiio  ad  altitiidiiiciii  0  deciesceiitem,  ipse  iiilerea  coiiliiiiin  attendi  ad 
opposittiiii  Holi  circiiluiii  (iiiterposiii  etiaiii  ideruuii|ii(!  (raiididissimaiii  papyium^  ab  liora  paeiietertla 
lie,  si  f'oi'cl  [traeccii patio,  initiuiii  iiivisiim  praeterlaberetur.  Taiilmii  veioiibfiiit  ut  teiiipus  praeni - 
ciipatum  I'lierit  <iuiii  retardatiiis  Ion;,'i'  Cult,  ipiaiii  onuies  sive  Tabulae,  sive  I'lplieiiieridi  s  iiidicarcnt, 
I'raetereo  autc'ii  per  id  toiiipiis  nnllaiiiextitisse  macula m  in  '^^.  Cuin  jiriniiun  piuiociri'iiliisteiiK  raii 
siirsiim  ad  dextraiii  est  visits,  reipiisiv  i  ex  laintilo  >Siili4  altiludiiieiii.  itcspiindit  ipse  monieiito  povi 
earn  esse  2S.  ;;rati.  30.  111:11.  iimie  indicat  t  est  bora  4.  in  in.  n'  .•■  "luiii  veio  inter  dij;ii(iM'eiiiliiiii  innn 
esHct  vei  iiuaciiam  luarsiiiis inaetpiaiitas,  vei  iimbrii  d  siilueiis  {iidile  &  inter  rtspoiitleiiiiiim)  laiitiim 
teinporis  est  clapsum,  lit  taiitiilns  iiiteit;i  del'ecliis  occiipave  potiierit  ,,',„.  iliametri;  idciKci  visum 
est  iiiiliuni  posse  exipiisilc  rert'ii.i  ad  iuu.  4.  iiiiii.  44.  en  nunc  sciiciii  olisei\atioiiis,  ciim  ilediiciis 
per  cftlculiiin. 


»4 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


[ 

I'nitcs  ion.    Siiiei  n.Mliirll>inc 

ilinmclri  ilc- 1      in     iliuili'S    cl 

ticlcniCT.     1      iniiiulu.             j 

1 

frniliiscircilin- ' 
crciitiftchciiu- ' 
mil'    ilolii  icn-  [ 

El    ilium.     0 

iiilf  colli- 

suitjM'slta    30. 
L'ltiitdmm.                           , 
in.  74.  sec.  (Ill-  ; 

1'"""""  "      liKl.ur    .Hum.  1 

«•                     i 

MUtuiIort  su- 
ra hnri/ontcm.! 

M»iiicnln 
Inrtc  clirila. 

1 

.Kg.      Ml. 

urail. 

mill.    Mc. 

K'-       '"• 

hor.   min, 
4.     44 

Initio. 

I 

1 

38.      30. 

5- 

<).    36. 

.8.             ; 

06. 

29.      II. 

28.        0. 

4-     47- 

7. 

0.     50. 

20. 

77»- 

23.     31- 

27.      40. 

4.     49- 

10. 

I.     la. 

25-       ; 

89. 

27-       3- 

27.      20. 

4.      5'- 

It. 

1.     26. 

28. 

95i- 

29.       2. 

27.        0. 

4-      524. 

14.                  I.     41- 

30.       j 

93. 

28.      16. 

26.      37. 

4-      5fi. 

18.                      2.       II. 

35-         . 

104. 

3'-     37- 

36.      Ill, 

4-      57- 

ao.        1        a,    34. 

37. 

101. 

30.     42. 

26.         2. 

4.      58. 

aa.               a.     38. 

38.         1 

14l. 

28.     44. 

35.     30- 

5.        I. 

25.               3.      "• 

1 

40.       ; 

OOj. 

27-     31- 

25.    24. 

5.        >i. 

a7.                3.     14. 

43-         1 

99- 

30 .        6 . 

25.        0. 

5-       4. 

30.                3-     3f'- 

1 

45.          1 

qf.j. 

29.      20. 

24-       40. 

5'        5- 

33.                3-     58. 

"• 

95- 

28.      52. 

24.    25. 

5-        7- 

36.                4-     IQ- 

50.         t 

99- 

30.        6. 

24.        5. 

5-       9' 

39-                 4.     34- 

51.        ! 

97. 

29.      29. 

23-     40. 

5.       M- 

39-         j        4-     41- 

52. 

.,8. 

39.      48. 

33.     30. 

5.       12. 

3gi.      '<       4.    45. 

52. 

9f'i. 

aq.      20. 

23.       30. 

5.      13- 

41*.      ;       5.      0. 

54. 

99. 

30.        6. 

23.         0, 

5.    15. 

4aJ.      j       5.      6. 

55- 

too. 

30.      24. 

22.       55. 

3.      I5i. 

46  J 

5-     35. 

57. 

97i. 

•   29.      38. 

22.       30, 

5.      18. 

47- 

5.     38. 

57- 

,/,J. 

29.      20. 

23.       15. 

5-      19. 

50. 

6.       0. 

(>o. 

100. 

30.      24. 

33.         0. 

5.     21. 

5S- 

6.     36. 

65. 

I04t. 

31.     4''>. 

31.         2. 

5.      26. 

bo. 

7.      12. 

67. 

101. 

30.     42. 

30.       30. 

5-     ag. 

bli 

7.     23- 

68. 

JOI. 

30.     42. 

ao.     30, 

5.     30.      ! 

6a.        i       7-     *(>■ 

67. 

()8. 

29.     48. 

20.       3. 

5-     3>i. 

'       62                    7-      26. 

68. 

looi. 

30.     33. 

19.     45. 

5-     33- 

f>4.                  7.      li- 

68. 

98. 

29.     48. 

19-     3'>- 

5-     34*. 

ft;.                  7.     48. 

70. 

lOOj. 

30      33- 

!     .9.     25. 

1 

5.      35. 

W)».                7-      SQ- 

{           7". 

99. 

30 .        6 . 

1     19-        5- 

-     5.      37. 

(17.                  8.       2. 

71- 

100. 

30.      24. 

18.      55. 

5.      38. 

68.                   8.      10. 

72. 

101. 

30.      42. 

18.      36. 

1 

5-     4". 

1       67J.                 8.        6. 

1           '"■ 

i        98. 

39.     48. 

i      18.        0. 

1     5-      43. 

68.                   8.      1". 

!     70. 

I        98. 

29.     48. 

!  17.  16. 

5-      47. 

68.                  8.      10. 

1     70. 

,        98. 

29.     48. 

1  16.  40. 

5-      SI- 

67.-               8.       2. 

;     69. 

1        97. 

29.     29. 

1 

I 

6f..                  7.      55- 

i           68. 

'J6J. 

39.       20. 

16.    0. 

S'      54*. 

62.           ,          7-      2fi. 

68. 

looJ. 

30.      33- 

;           15-           30- 

5.      57*. 

'      50. 

7.        5. 

66. 

i      u». 

30.     24. 

,     15.        0. 

6.        0, 

i      58. 

6.      58. 

65. 

90J. 

30.      15. 

j     14.      4". 

6.      12. 

'    a 

fi.      36. 

64. 

loa. 

31.       0. 

1     13.      58. 

6.        6. 

i    »•• 

6.      15. 

60. 

96. 

29.      II. 

j     13-      35- 

6,        8*. 

1       |0.                   <i.        0- 

5<). 

97. 

29.     29. 

13.     25. 

6.        9».      , 

41.                   5.      4'>. 

58. 

j       98. 

29.     48. 

13.       5. 

f , .      II.        1 

.     46.              5.     31. 

57- 

'W- 

30.       6. 

12.       48. 

6,      (3. 

n-          ».  4t- 

5t' 

1       .07. 

Ju.      32. 

S4-                4-       S- 

4<). 

1 

86, 

36.        9. 

' 

t                    • 

RKSEARCilES  ON  Tlir;  .MOTION  Ol'  Till;  MOON 


l*arleH  loti. 

dUnictri  dv- 

ticicntes. 


3'. 

28. 

27- 

as- 
23. 

20. 
iq. 
17. 
12. 


Sen  ei  tciliirliin 
in     <iiKilns 
niiiiuta. 

iliK.      m. 


•  rndnHrirtum-i 
tcrcntiiie  hclnt 
ct   indc    ilvtideii' 
Its. 


Kt   cllam.    O 
Unilc  colli-     MippiiHiia  10.    Altiiijil"  0  su- 
Kltur  illam      m.  .•!.  see.  ti.l-  p,,  |„,ri/,micm 
i>nrlitin)    ^    .  Iii;itiir    diain. 

min.     Hcc.  Rr.       in. 


54- 

43- 

24- 

14. 

0. 

2. 

4''. 

2. 

24- 

2. 

17- 

2. 

2. 

1. 

26. 

48. 
47. 

44. 
43. 
4". 

38. 
37. 
35. 
33. 
28. 


102. 

103J. 

100. 

W. 

Sr). 
lOI. 
08. 
92. 
<)ik 


3>. 
3". 

30. 

3". 
27- 
27- 
30. 
20. 
27. 
2.). 


28. 

2|. 

fi. 

3'. 

3. 

42. 

48. 
58. 


II. 

10. 

10. 
10. 
10. 

8. 


37- 

27. 


45. 


<)■     3". 

,).         o. 


MoiiiL-nlii 

itxic 

cUiita, 

hor. 

min. 

!    f>. 

22. 

f>. 

23*. 

(k 

25*. 

f). 

27. 

(1. 

2.S|. 

<<. 

2<)i. 

1 

31. 

(>. 

3U- 

6.      35J. 


IlttctoiiuH  tenuiora  solum  i\ul)ilu  foci-iant  ncKotiam;  e.\  hoc  vei<>  toiiipoic  .siiliortu,  ac.  sfiisim 
u.scouaeiis  ab  occasii  ora.ssi.ssiinivmibos  ita  Solom  snhiit,  ti-xitiiinMit  laotii.s  cxiiidi'  liuuit  iiit-oii 

spicmis. 

Soqnitur  Huliiaiai  observatio,  quao  o.st  in>nifta  I'.irisiis,  opiiosito  Moh  circuli),  ciijiis  (liaini'tcr 
fsset  \n\ew  bos  lu'.li.s  P,ui.si»'nsi.s.  Et  ilianu'tnim  ilivLst'iat  (luitU'iii  in  partei.s  2  j.  ciiciiliim  in  part.'i.s 
iSo.  atiinod  sohjs  VU.\m'\>*  notari't,  altitu.liiu's  c.ipm>t,  vS:  sinRula  opi'iaretiir,  noii  pofiiit  HJinul  ml 
.liainctroruin  incliiiatioiioH  attonilere.  (iiiml  supcn'st  obsorvationcin  i-citmn  ad  miniituin  liaU.MHla.n 
pcrsc.ripsit,  &  bac  Ibrina  ad  mo  traiisuiisit. 


AlliliuliiiC!! 

Mumcnla 

AUitudines 

parall.  it  Refract, 
corrcctae. 

ex  altitiidlnibus 

Diftiti 

0  obscrvatc. 

corrtctis. 

rCcliplici. 

gr.     m. 

grad.  min.   sec. 
33.     35.     59. 

hor.  mill.   sue. 



3a.     35- 

4.     21.       4. 

Cocpit  ({  Miliiucii- marBimm  0 

31.     30. 

31.     30.     5". 

4.     27       39- 

H. 

»8.     57- 

28.      57-      25. 

4.     43-      >2. 

4.    0. 

47.     56. 

27.      5f>.      2»- 

4       4').      24. 

5.    0. 

id.     56. 

2f).      56.        7- 

4.      55.      31. 

ft.    0. 

35.      13. 

25.     II.     3''. 

5.        0.        8. 

7J. 

33.      55. 

23       54-      >')■ 

5.      14.        0. 

8.     0. 

1 

21.      51. 

21.     4'>.      37 

5.      2(1.     47. 

Si|. 

!lfo\im(i«  'lrt('(Mn<                                        j 

2<t.         0. 

l<).      57.      44. 

5.    38.    i;- 

S.     0. 

1 

18.       30. 

18.      47.        7- 

5-     45.      '4. 

7.     0, 

IS.       8. 

18.       4.      35 

5.     5".       3- 

ft.   •. 

. 

16.     36. 

Ui.     31.      31 

5.      S')       4fi. 

■,}- 

*».        2. 

1       15.     57.      '7. 

6.        3.      37. 

4.    «. 

'5.      Sf'. 

15.     3i.        •• 

6.       6.        5. 

J*- 

:  15-    s- 

15.       0.     53. 

6.        -,.      ■<>• 

3.     •• 

14.       2^1. 

14.     20.     31 

ft.      13.      33. 

a.    OL 

13.      3S. 

'       13.     3a.       "■ 

6       18.     43 

I.    0 

12.     41. 

j       13.     ».     49- 

e.    2|.    4g. 

0.     1. 

("iiiis     >•■!  \»ttmt^  ■«»  scrnpul"  cinm*. 

1 

._« 

_  ,  -         -.            - - 

S6 


Ri:SKARCIIi:s  ON  Tin.  MOTION  OF  THE  MOON. 


ICcliiinf  <)/  if>5:,  Ajifil  7,  ohscrrnl  a  I  IHgiic. 

I'l^:. — Mfiiso  .\|ii'ili,  i1i(sS.iinU>  iiiniilitMii  r>i'li(isi!<  O  Diiiiau  iii)v«!iiili>(;iiii  iiiitr  aiiiii.<iiliiM|iioi|iii' 
Ajirilis  S,  nli.^i-rvilriiin  iiliain  hiio  Hiipnriii.^  loRo  tlescriptjiin.  ]0:i(hMii  siitii  proitiiln  iihiih  iiDKrIiiiia, 
iMiliMii  <i1isiM'va!ii1i  riilioiic;  iii.si  i|tii)il  \- hiumisiiu  c<>IIi)(miii1;u>  ir.iicliiiiac,  iS:  Iikmuii  pri)xiiiiiiiii  (liipliimliM 
Siilis  iillihiilinibii.s  in  ipsi.miicl  I'riiopo.sitiirat'  acililms  apparavcrarn.  i}iun\  pi'ovidis.scin  )ii)ii'(>  tori-, 
III  liiii.M  (>clipsi>i)s  .suit  ini'i'idii'Mi  ciiiitiii^^crct,  ac  proimli'  fcnipiis  ex  paniiii  vaiiati.s  Soiis  altitmli- 
iilliii.s.sati.-<c\i|ai.'4iti' ili.sccrni  iion  pi)s.s<>t;  idcirco  appararaiii  Si:i()tci'i(!iiiii,cpio<I  i|iia.-<p()s.'<(>t  Niippi-tia.-* 
ipsi.s  alliliiiliiiibiis  fcrri't.  'iuod  vcrcrt'i-  aiitoiii,  nc  iiiKiavi'S(!i'iiti',  (jiiao  al)ali<piot  tlicliiis  iiii>  lial»i« 
l):il.  ft'l)rit:iila.  adi's.sr^  ohscrvando  noii  po.s.sou);  id*>o  (■oiiiiiiiin.sti'Aniii)  nnii  iinxlo  Taxili,  Toniatoii, 
lid(i<pu>  Aaiaiiiii'iiHiAiitoaio  I'i)ti>ria(>,  sed  itiMiipiM'  rtiaiii  Javciii  pi'acclaro  (''njiciscM)  ntTiicrio,  qiiciii 
totiM  diii)l)ii.s  iiKMi.HJIiiiM,  ciirn  nic  iiivisi.ssi>t,  j.iai  dctincldiii,  (|'iiil  iiaii;ui(|iii^  pracslaiidiini  foivt,  iit. 
iiiivio  vi(M's  siippliM'ciitiir.  l'',iir  inilii  taniMi  pr.)pitia:ii  iinai  <ii,  iit  pxHi'ii  n  ):i  m  )  Id  iiiti'iv-isn,  scd 
iv};i'r('<pioc|ii»'  iiida  lyiiipaninii,  ciiTiiliiiii  eflip.scds  t.vpiiin  ('xliilicntcin,  iitpoto  oxcipiunlttin  tr.ijcdto.s 
ti>lc.siMpii>  una  caai  tiiaii)r(^  iiiiihrai'  liiiiari.>i  S;>lis  nidio.s,  ix;  a.lai>t.iri<  Hiiniil  fi)i'ai  ini,  i|iiiiiititii- 
t(Mnipi4>  ip.HJii.s  doli'ctiis;  iidjatahat  vcro  adnotautn  praetor  ToriiatortMn  cxiiiiiiis  .loaiiiics  l''raiii;is(Mi.s 
Aiig^HiiiH  Ito^ius  cojjiiitor,  &  riMiiin  lioimniiii  appriinn  stiidiosiis,  ipii  iiiii^  ciiii  opliiin  Ij-iiitnrntio 
(li>n  i>arti(M'ps  spcctaciili  voliiit.  .Mudi'r.ilialiir  intcrc.i  l>>>rMi>riiiH  iiiacliinaai  inaiitilirio,  Taxilis  extra 
s:-t>iiaiti  (pi'iilratiiai,  Potcria  ad  <piiils'is  I'ainiilili.tlni'.  N<>  loa^iiin  aiil'in  f'.t(;ia!ii,  nvii  totain  pro 
ii)()r«*  sic  iiao  pn>.'4i>i>clii  ah  ocuIom  pono. 

Cam  Icinpiira  lit'it'  lialN-antur  ex  Knli.s  altitiidinilxis  dfdiicta,  taccii  iioii  di-liot  SciotcricMiin 
(>\)iilMiiss(>  initiiiin  diiolais  propc  iniiiiitis  aiit<>,  IIihmii  dii(>l)ii.><,  uiit  tiil)us  po.^t.  Kt  i|iir>d  ad  initiiiin 
i|iiid<>in  attiiict,  altiliidiiii  iiiauis  lido:  (piod  ad  liiifiii  aiiloai  sju'ctat,  inaKi''*  liaccrt'o;  ac  ]>(>tiHsiiniiin, 
ipiia  Mii'iiiiiii,  tainct.si  |irip<>iidicu!iiMi  vi.siiin  est  coiLstaiitins  liacrcrc  ad  partem  uad)ra(>  vcrHao  711. 
ixi'iirriN.s«  tarwn  iiitctlum  vtMsns  740.  it  ad  .Siiotcriciim  cum  rcspoxi,  iiinhra  styli  Hatl.s  jiraocisc  ad 
mciidiaiiaiM  liiicnm  i|iiadrali:il  ;  ipiod  cxc-fssi.ssc  t>iiim  pilsim  vid*'l>aliir,  id  spoctarc  poliiit  ad  toinpii.", 
ipii)  ail  i|iiadiatiim  luc  attciiliim  pradiiii.     I'tcuinipio  fiicrit  ex  dcdneta  .■•iTie,  (M)iili;.'it  ceiiiiseiw. 

Iniliiiin  lior.  9.  iniii.  43.  iiiediiim  lior.  10.  niiii.  51.  IIiiih  lior.  n.  iniii.  5^. 
Si('i|iio  fait  tnta  dnratio  lior.  j.  miii.  15.  dimidiiiiii  lior.  1.  miii.  7'  .. 


Here  aiiiciii  maxiiiiae  oiiNciiralioiii.s  di};it.  9.  miii.  <|. 


Diainetrorum  prnportio  satis  inconstaiiN;  veriiiitaiiien,  tie  eain,  ipiae  lialietiir  cirra  initiiiin,  ac 
liiii'iii  inoror,  videliir  omnil)iis  expensis,  iV  oli  I'iiaseis  alitpiot,  ipias  coaimemiiii  dill;;eiiliiis  notatan 
p  isse  rem  ila  deliiiiii.  at  si  diameter  0  snpponalur  I'lii.^se  min.  31.  .see  \.  diameter  ([  tiicrit  mill.  ■,>'• 
sei\  55.  sin  ampliiis,  aiit  minus  pari  )ir()p<U'li()iie.  liiiliet  porru  nppoiien-  .sclieina,.iiixta  qitod  propor- 
lioiieiii  dediixi. 

(.'iitn  snltiiide  oti.M'i'valioiH'm,  calctiluii.tpie  eelipscos  eoaiaiuiiicas.sem  cum  optiino  X'aicsio, 
resci  iliciis  ipse  die  .17.  (iialiiinopoli  per.sciip'<it  treis  olis.'rvationes  diMs  I'.irisiis  si'orsiai  peraetas, 
alleram  a  iiostro  itiillialdo,  allerani  a  iiieii  (pioiKlam  A;,'ariatii 
iioliili,  (M)miiiuniipiu  iioMtro  San  l<e;;erio.     I'arisieimis  xic  rueriinl 


Miirino:  lertiaiii  Avciiiuii>  a 


lliilllMldd 


A);!irnil<i  iV  Muiiim. 


nilinrn  lior. 


47- 


.Medium  lior.  10.  min.  25,  hoc  19. 
I''iiiis  liov.  II.  mill.  |2.  Hec.  14. 


lior. 
lior. 
lior. 


9.  null.  30, 
10.  iiiiii.  45. 
12.  mill.  1.1. 


Inilinm  lior.  9.  min.  ;i^. 
\\eiiioiii-iiHiKaiitein  sic  ]  Mi'dium  linr.  10,  mill.  50. 


s 


/ 


t'trlqili-. 

I>i;;iii  eeliptiiM  10.  mill.  70. 

I)e    ipiantit.ite    ei^lip.scoN 
nihil  perseripHit. 


i''iiiis  lior.  1 1. 


mm.  5,3. 


« 


RESKARCIIES  ON  THE  MOTION  OF  THE  M(X)N, 


«7 


liilipsi-  oj  ifisj,  A('iil  7,  I'l'sctvi  (//•}•  CiAssi-Nins  at  Di^iw. 


l>h»M8 

Alllt 

11I0  0      ■■ 

Ti-mpiira    j 
Inde  clk'lta  ' 

ScmlurcllA 
(Ifficicll-  j 
llnoruo©! 

OiiRlluni 
Unmet.  0, 
71^1  titlitl 
cliiiiiir 
ftcmi- 
dittinet.  C 

(Idiic  iliaiii.  0 

30  mill.  4c.«it;f.  1 

flciltii-ltur 
Acniitliiiin.  C 

Ac  pn.iiiilc 

ipSli  HCIlli- 

iliutiictcr  ti 

ilo(cctu> 

Umbra 

rcctR 

Uillltl 

92500 

gruil.  iitin. 
43     46 

)ior.  mill. 
9    43 

Rriid. 

mill.   MC.      1 

111)11.   «vc. 

Iniliu 

. 

oj 

930 

43    la 

9     46 

16 

638 

26    45 

13      22 

I. 

955 

43     40 

9     49 

34 

764 

33     33 

16      16 

It 

9f.a 

43     54 

9     51 

29 

7^4 

30   50    i 

15      3S      ' 

3. 

977 

44     20 

9     54 

34 

748 

3"     5'J 

>5     55- 

aj 

901 
V.V. 

44     44 

9     57 

38 

740 

31     31      ^ 

15     45 

3. 

999 

45       » 

10      0 

43 

751 

32      0 

If,      0 

3i 

99' 

45     16 

10        3 

45 

719 

30    38 

15     i'> 

4. 

977 

45     40 

lu       5 

48 

6g8 

2')     44 

11     52 

4i 

965 

46       1 

10      8 

5» 

743 

3>      39 

15     5" 

5. 

948 

46     31 

10     13 

55 

74a 

31     36 

15     4« 

Si 

935 

46    54 

10     15 

58 

739 

31     2() 

15    45    ; 

6. 

9»4 

47     «4 

10     l8 

fioj 

730 

31       6 

15    33 

t-i 

9"5 

47    3» 

10    31 

64 

746 

31     4f' 

15     53 

7. 

goo 

48      0 

10     2; 

(.7 

740 

3.     3. 

15    45 

74 

8()i 

48     .7 

in     28 

70 

749 

15     44 

15     57 

8. 

S78 

48     43 

JO     32 

73 

751 

32      0 

16      0 

84 

865 

49      9 

10     37 

7.6 

750 

31     5<' 

15     57 

<»• 

84y 

49     39 

10    42 

79 

748 

31     51 

15     55 

•iA 

938 

50       3 

10    45 

3o 

719 

31      54 

15     57 

qA 

838 

50     13 

10    48 

81 

753 

32       5 

1(1        3J 

9A 

834 

50     30 

10    50 

82 

753 

32       5 

Id        2 

9i*j 

S22 

50     34 

10    ji 

»2 

753 

,      33      5 

IC        2 

9  A 

820 

50     3S 

lu    52 

S3 

763 

33    37 

If.      14 

9/11 

8-1 S 

5"     43 

I"     53 

82 

753 

32       5 

Ifl         2 

Ql'tt 

IH4 

50     5> 

10     55 

81 

-f'5 

32     35 

15       >« 

9> 

«^ 

*l       • 

10     58 

80 

762 

32     37 

III       14 

^ 

7W» 

SI     M 

II      3 

75 

7U 

31     34 

>5     47 

S. 

787 

S«     47 

II      8 

73 

751 

,       .■'2      0 

lO       0 

« 

7* 

ii       > 

i    II    n 

6,, 

734 

31     16 

15     38 

i^ 

'   a*- 

»    » 

u   t* 

(-Si 

7S3 

30     47 

15     24 

« 

^   w* 

'   Sft  n 

M     1» 

('3 

72(1 

.3"     55 

15     27 

•». 

-^ 

1  »  » 

«     n 

60 

7J(J 

3"      1" 

15     20 

# 

lift 

m  -m 

•t     » 

S» 

739 

.u    39 

1     "     1 

i> 

i»- 

s»  n 

!  It  m 

» 

742 

)»      ♦'' 

15     48 

4k 

»i> 

m  9» 

i<    3B 

5^ 

775 

33       ' 

iG     311 

*. 

7i» 

ss    « 

M     ^ 

;      41 

753 

33       5 

i(.       2; 

3t 

7W 

i    S3    *• 

m    ft 

4* 

n» 

33     51 

Id     Qi 

s. 

TW 

'    S3    H 

'    »    «• 

"'      * 

7S« 

32      ') 

III       >) 

«t 

»« 

S3    *« 

i      M     ■^ 

3« 

740 

31     3« 

15     45 

*. 

■$m 

n  w 

!     W     4? 

M 

JlS 

31      «,! 

1     '5     » 

I* 

m 

,  ss  m 

'     »■    « 

W 

T43 

27      34 

i     13     42 

** 

1    ^ 

i    S3    as- 

t»    s» 

»3 

(72 

23      2i> 

,     14     30 

«» 

S3    » 

ii    u 

H> 

Cj? 

30     45 

13      23 

,  :m 

»   a» 

1 

.1 

1 

i 

j         ■         • 

1 

1 

1 

i 

.  — —  - 

■  -   - 

88  RESliARCIIES  ().\  Tin;  .MOTION  OK  Till.  MOON. 

Obsenalio  lUliqmt  So/aris  die  n.  Aii^iisH  i6^^. /li/iiis-StJC/iit /iiitit  ai  J/ononilo  Galleno. 


DlKiii 

Inliin. 
I. 

I. 
a. 

t- 
3- 
i- 
4. 
i. 
<6- 
i. 
6. 

i- 
7. 
J. 
8. 


Aliltudo 

© 

Kf 

iiiin. 

3S. 

30. 

3f'. 

15. 

38. 

35- 

39- 

45- 

41. 

lo. 

41. 

35. 

4a. 

35. 

■43. 

6. 

4$. 

35- 

47. 

14. 

48. 

10. 

icu ratio  SolU 

r.i 

RccupL 

ratio  luminis 

1 

V. 

T 

CIII|H) 

Altitude 

0 

V 

Tcm|io 

.J. 

Kr.  niin. 

liiir 

III  ill 

sec. 

OiKili. 

Hf.  mill. 

gr.  iiiin. 

lior.  iiiin, 

a.     18. 

SIC     1 

S4.     S7. 

3. 

39. 

.9.1 

49-       7. 

34.     «7. 

53-     3'J. 

3. 

34- 

')■ 

. 

50.  30. 

51.  10. 
53.       2. 

33.     35. 
30.     58. 

21).       15. 

3.  1). 
3.  4. 
.'•       57. 

10. 

. 

sa.    2(i. 

37.    37. 

1.      49 

(.. 

50.     3a. 

3- 

32. 

3. 

53.     12. 

27.       31. 

1.      49. 

2, 

48.     50. 

3- 

15- 

5. 

53.     50. 

26.       8. 

I.      44. 

46.     46. 

3- 

7- 

54.     21. 
54.     55. 

25.     <). 
34.     I. 

1.      40. 

I.      3<>. 

1.     1 

46.       8. 

3- 

1 

s. 

55.    au. 

23.       9. 

1.      33. 

9. 

4I.     40. 

2. 

58. 

lu. 

55.     33. 

33.      43. 

I.     y>. 

13. 

43.      53. 

a. 

55- 

t. 

55.  r8. 

56.  18. 

31.       50. 

21.       14. 

1.  37. 
1.     35. 

5. 

40.       6. 

a. 

40. 

b- 

57-       • 

I.).       31. 

1.     18. 

. 

37.     30. 

2. 

30. 

. 

Finis. 

57.      30. 

18.     45- 

1.     15. 

36.       5. 

a. 

24 . 

1.   t 

' 

• 

liiitiiiiii  liiir  H.  mill.  20.  nit'diiiiii  lior.  i).  min.  ■}(>.  Urns  h.>r    in.  nii.i.  4;.  tola  liiiiatio  lior.  2   mill.  3;, 


OIJSKItVATIONH  UP  HEVKLIUS. 

Tlie  olwiviifiiiii.s  »it'  IIkvkmi  8  artj  touiid  in  tlio  MuiliiiKi  Cdvlr.stii,  pars  po.storior. 
Owiii/i'  tn  tlio  furity  nl'  t\\U  work,  the  o1)sorviitioii.-(  I  luivo  iisod  iiro  <rivoii  protty  fully. 
Tho  portitioii  <it'  IIkvki.iisV  obrttM-vntory,  fnnii  data  kindly  coiiiiminicatod  by  Dr.  Kay- 
8KK,  was 

Latitude,      54     21'   19";  logprfiii  </>'=  9.90795. 

Loiifritiiilc.     i''   14'"  36"  oast  of  Givciiwicli ;  log  p  ctm  </<'  =  9.76644. 

KrIipHiH  Solis.  1639.  .hinc  1. 

The  tiiiK's  an:  from  a  sun-dial  ("u.x  Sciatorico"),  wliicli  must  liavo  Iiecii  wlitdly 
uiifclialilc.      1  tlitTi'forc  make  no  us(>  of  tlio  oliscrvations.* 

I'iijj,'  ■J. — OltHcrvntio  H(!li|wc().s  Palilicii.     .\iiiio  1^141,  ilie  15,  Novciiib.  iiiaiu'  iiiHtitiitii  <UMluiii 

liiilititii  OiTiiKatioiiis  I'alilitai  u(;(;i<lol)at  NctniiHlain  liiirolo^riuii)  coircctiiiu  (altiliidiiiL'H  oalin 
tinii  t<>|i()i'is  iiliHcrvaiKli  noii  ilaltatai'  (ii;ca.sio)  Intra  3.  iicitiit.  5'-  Occaltaliatiir  i\  Laaa  circa  96.  {;i'ail. 
linilii.  iM-in|ii'  oriciitalis,  ad  .Moiitciii  .Malia.striimia  Mai'i.s  I'iol;  <|ii()  tiMiip.iru  gradas  liiiiia'  75.  liiubi. 
viTticali.'*  cxisti'liat.  JCincrKt'liat  lior.  4.  5'.  30".  circa  j;ia(laiii  317.  liiiiUi  occiilciifaliH,  MonteiiKj;  Alan- 
iiatii.  iiaiiliilt'iiii  KUpra  Palixlciii  .Macotideiii ;  qao  tciniiori.sarticalo  f,'radii.s  liinlti  Laiia>  78.  Crat  verti. 
cali.s.  Ilt>rii4. 10'  1,0"  pof^t  cmcrNioiioiii,  I'aliliciinii  taiilo  spalio  a  liinlto  rcinnvcbatiir,  i]aaiiti>  Kcilici-t 
lai.t  <*rat  I'ahis  MuMitis,  partu  iiiaiin'iia  damli'ciaia  circilcr  diaiai  'ri  riiiMiu'i.s. 

.\s  tlir  altniidcij  ffom  which  these  times  are  deri  lod  are  nut  ;.iiveti,  wi'  have  to 

iU^  the  uin'»Mt;iinty  of  tlit;  elements  of  reduction  ii.sed  hy  IIkvki.iih  to  that  of  his 

*  I'bis  reiuari  <hu  niaile  ni  the  lime  n(  ftrst  examining  the  jliservationi).  .Aflcrwanl,  li.iviiig  come  inin  iHisucssion  or  a  copy 
••f  the  iintjiii.il  work.  I  concluilcil  lo  reduce  llieiii,  more  .is  nn  expcrimcnl  llian  wilti  llie  li(i|ie  of  re.uliinn  .my  result  of  vaha-, 
ami  llie  ri'sulls  an  ^'iv-  ti  in  a  ..u!isei|uciil  sectimi. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


89 


olmcrviitioiiN;  1  lmv(!  tlicnffonf  lit'sitiih'*!  wli(«tli('r  to  uso  tlic  oltstTvatinn,  but.  (Hnicliulcil 
to  do  HO  owiii},'  to  its  i'urly  t^iMU-li.  Tlio  filiation  of  tiino  \\m  —14'"  51",  wo  liiivt?, 
tlmrotorc,  for  t!ie  nu'aii  tiincH:  — 

Iminuniloii.  Kiiivriiinn. 

Apitiirent  tiuK'H  ifivon  l>y  IlKVKi.iim      .     .     .     15''    5'" 

Moan  tiiiU'H  tliuuco  di'diicod 14''  50" 

Oruoiiwicli  mean  tiiiicH       '3''  35" 


0" 

16"     5""  30' 

9" 

1  5"  50'"  39' 

3" 

14"  36"'    3*. 

Lclipsis  Siilis. 

Anno  Afrae 

C/iristinnae  tl 

45 

,</ 

If  »i.  Aupt 

S/iS 

t.  n.     Gittani  obsenan 

1. 

Crescentis  Uliscuralionii. 

Decrcscentis  Oliscuratior 

is. 

Secundfl 

1 

arciirain  Scialc- 

Altit.  Sniis 

Ttmpiis  ex 

Phases, 

rlcfi  liiicac 

Meritliaiiacappli- 

caliim. 

yiiad. 
Orichalc. 

allitiidinihiis 
correctuni. 

Phases. 

• 

h.       m.      1, 

•                1            i> 

h.    m.     s. 

- 

1 

! 

_ 

Inillum 

n.     aj.    4S. 

. 

. 

7}- Dig. 

45-  30-  '     - 

tDig. 

II.     37.      0, 

. 

7J- 

50.  40.        ... 

j      . 

II.     3'-     3"- 

47.     15-      "• 

II.    31.      (>. 

7- 

54.  45-   [       -        •        • 

'li.Dlg. 

II.     33-     so- 

. 

6i- 

1.   50. 

1     a. 

il.     38.      0. 

. 

6. 

h.     (1.      45-    41'       "'• 

1.     6.     8. 

St. 

II.     .»3 .     30- 

. 

Si- 

8.    30. 

3t. 

II.     45-     so- 

. 

Si - 

13.    20. 

4t. 

il.      5fi.       0. 

•  .     • 

4t. 

15-    3f>-      45-     5-     0- 

1.    15-   J'l 

5- 

13.        1.     30- 

. 

3(1.      0,             ... 

• 

Si- 

13.       7-     30. 

. 

4. 

33.    45.       44.    3'>-      O- 

1.   24.   25 

<      6. 

13.       II.      30'- 

. 

3- 

31.    3«-    ;        -         •         • 

^. 

.3.       If>.      30. 

. 

i- 

47-    30-           -        .        • 

.   f-i. 

13.       31.        0. 

. 

i. 

41).     0.           ... 

7- 

13.       33.        0. 

. 

Finis. 

53.     ».           .        .        . 

7l. 

13.      35.        0. 

. 

5f).     0.      41.    55.     "• 

I.    55-    50 

7i- 

13.       37.        0. 

. 

36.     0.      38.  *(>■     "• 

3.    3r>.    40 

71. 

13.       30.        0. 

. 

• 

30.     0. 

38.   34.     0. 

3.    30-      0 

1 

7i. 

13.     31-       0. 

. 

• 

• 

• 

, 

13.      3fi.     3<'. 

47.       0.      0. 

13.      37.      13.    1 

.    1       . 

71 . 

12.       41.      30. 

4f>.     50-      0- 

i 

12.     41.     53. 

• 

'   [       '       ."_ 

■ 

Tlio  ^un's  di'dination  at  110011  Wn\»  -f  11°  59'-0»  ♦'»'  lioiir-an«rlo«  f,Mv<'i»  in  tin-  lant 
.•olunin  sc'Oin  very  nearly  corivct.  'I"iu>  jrcMioral  a^r,-(.<.incnt  of  tlic  .Hun-dial  with  tlio 
times  dedneed  from  the  altitudes  aiVords  a  Mroiij-'  piesumi.tion  in  favor  of  the  acenrary 

of  both. 

The  following'  arc  thecorrcctions  to  n'diiic  the  -mi-dial  to  moan  time,  as  d.-diiccd 

from  the  nine  individual  altitudes: — 

-f  1"'  50"  5"'  iS"(0 

3""  30"  2"'     5" 

3"  '9"      ■  3"'  a'" 

3"   i2»  2"'  48". 

2"  53'      - 
VI 75  Al'.  J 


90 


RKSKAKCIIKS  ON  THE  MOTION  OK  THE  MOON. 


Ill  tlif  ciisn  of  till!  sixtli  altitude,  thorn  is  fi  (lisfrepiiinry  of  two  iniiiutcs  Ix'tweon 
tlio  i'lUH'H  '/\\{'n  liy  IIkvki.ii'h  and  tliat  ilcdiirililc  tVoin  tli(t  altitinli*,  which  woiiKI  Htteiii 
to  arise  iVoin  an  error  in  |)rintin<r  the  aUitmh!.     This  is  therefore  reje«"te«l. 

The  mean  r»f  tlieei^rlit  reniaininj;  results  is  -f  2'"  52",  which  is  the  constant  applietl 
hereafter  to  reduce  the  dial  to  mean  time.  The  eqinition  of  time  heinj;  2'"  31',  tho 
apparent  error  of  the  dial  is  21*. 

.Indjjjin;;'  from  tho  discordam^OH,  tho  prohalde  errors  of  tlio  ohserved  times  do  not 
(tX(UM,'d  15"  or  20". 

Paul!  M.— Occiiltatio  I'iililjcii  Ainio  ifn^,  iVw  K.  Oclol).  Ht.  n.  Lniiil  (•xistonto  (("■'''l-  ntMlmii 
aiiiiniiilvcrsii.  (jaaiii  Laiiu  I'sililicii  a|i|)ri>|ijii(|ain-ct  a<l  ilisiuiitiaiii  15',  unit*  Hcilicet  (MiiiJiniclJinieiii, 
•loviM  iiltjtatio  (jaadrante  I'.x  Oricliulco  con Ici-lo,  accural i;  ilt>|iri'lu'iiHA  est  in  |)la(;ii  OritMit,  36°  15' 


I'l'inciiiiani  oltscarati  I'alilivii  incidcUat  in  altitinlint^  ilovis,  38°  48' 


43" 


lOau'rucntc  riMsiis  I'lililico  «'x  ainlira  Lana;,  allitado  hunu'i'i  lucidi  Orioais,  in  pIhriI  Orient 
invchiflmtar,  38^  45'  . " .  2''.  57'". 

The  position  of  .lupiter  for  tlio  timo  «>f  immorsioii  hiw  been  dorivod  from  Uou- 
vahi/h  tal)los,  with  the  result:— 

Geocentric  rij^ht  ascension 6''   24"  34" 

Geocentric  dei^lination +  23°  4'.o. 

Hence,  from  th»!  secoml  altitude,  we  have,  for  the  local  mean  time  of  tlu»  immersion, 
'3*'  jX"  '^""  'he  e(piation  of  time  is  —  12'"  25",  so  that  tiiere  is  a  ditlenmce  of  more 
than  two  niiiuites  hetwcfon  this  reduction  and  tliat  of  IIevi;i,hs.  The  discrepancy  is 
tho  same  in  the  time  derived  from  the  first  altitude,  so  that  tiie  ditrerenco  can  urlHO 
only  from  the  difference  of  the  adopted  positions  of  .Iupit<!r,  or  other  data  of  reduction. 
Th(^  altitude  of  or  ( h-ionis  <;ives  for  local  mean  time  14''  43'"  20",  about  a  minute 
earlier  than  that  »»f  1Ievkmi:s.     'i'ho  results  «)f  the  roeomputation  of  times  are: — 

Groenwicli  mean  timo  of  immersion   .     .     .      1645,  Oct.  7,    12''    iS'"  30". 
Greenwich  mean  time  of  emersion      .     .     .     1645,  Oct.  7,    13''  28"'  44".       '• 


o 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Obsenalio  Edifsfos  Solaris,  Gfitani,  Anno  ,t,r.tf  Cliristianat  165*.  die  8  Afrilis  si.  n.  />,t<ulit. 


91 


Oriln  lllM.     Itla«luin  niRlll 


( rmti. 


ki«|itlcl. 


10. 


13. 


M. 


16. 


\i. 
19. 

30. 
31. 
33. 


«3- 
34- 

35- 
3b. 


Verum  al().  Ken-  Tein|»i«  'wci 
Vlbr«tlimr»  „!„„„  ,j|„_  „  t»,|ui-il4 
|icr|«nilu        ,i|„,ii„„il>iiH      lUiim    k 

•M. 


Nihil  adh. 
Iniliiim. 

3l. 

3- 
3i.fri*. 
3) .  A:  )>aul6 
.  plui. 


7- 


|)|US. 


.)i.l>i8. 
8i. 


(.■i. 


J5J. 

37')- 

507. 

6J5. 

853. 
laSr. 
1985. 

3155- 
3330. 

2484. 

3598. 
3681. 
3H36. 
3308. 
330a 
3503- 

3574- 
3657  • 

3750. 

3«3». 

3954. 
4130. 
4314. 
4370 

4588. 
4f>90. 
54f'« 

5590- 
5735. 


<8i6. 
6313. 
6488. 
6883. 
7103. 
740a. 


THiri 

p«n>. 

dcilui  lull). 

late 

10. 

3.   M. 

i(>. 

fi .    4() . 

lu. 

9.    44. 

10. 

13.    41. 

ID. 

>7.   47. 

10. 

37.  41. 

10. 

43.   55. 

10. 

lu. 

47.   51. 

(t.     JO 

umtbm 

TemiHira     fterft- 

ICWtC' 

ilfiin  li<>riil<if(i> 

trUiiii 

urn    iitilmlaiu 

rlum. 

— — 

tliiluillnH  lAriiirtliimTamp. 
uiuliini. 


10.      11. 
10.      (1. 


10. 


10.  55.  2i. 
10.  57.  30. 
10.    58.     8. 


11.  14.  30. 

It.  \(>.  36. 

II.  19.  o. 

II.  3<>.  39. 

II.  33.  34.           M.    33.      O. 


10.     13.  U. 

I     10.    n.  o. 

,         '      10,    3U.  » 

to.    JO  rt. 

I     lo.   4<>.  o. 

l«.    ;o.  o. 

10.    54.  o. 

10.    ;8.  o. 

It).   57      \.>.        II.     <>■  o. 

10.    o       o.        II.     o.  45. 


II.     3.   30.        II-     <>•    13. 
II.    14-   30-        "•    '7.   30. 


II.  16.  ;.. 
II.  19.  o. 
II.   31.     o. 


•I.   34.  43. 

It.   a6.  4<;. 

1 1       3q.  36. 

II.    33-  17. 

II.    J?  37. 

II.    S*"'  4J. 

II.    4t-  6. 

II.   4'>.  38. 

13.     4  19. 

li.     7.    '4. 


13.    I".   35. 


11.  19.   30, 

II .  21 .    18. 

II.  23.   58. 

II-  35-   53- 

"•   as.     •>-        I,,  rt.  a6. 


II.   37.     o. 
I        }i>.     o. 


II.   3"     39. 
II.    33     35. 


11.    3J.     o.        II.  3'>-  I" 

II.  J?    30        "•  SQ.  a" 

II.   V      o.        11.  40.  o. 

II-  47-  7. 

II  49-  .19. 


11-44-     "■ 

11.  4'i     3"- 

12.  4-    30. 


13 


13. 


58. 


O.    30.  12      13.    30. 


PH.ASKS  DECRESCENTES. 


13.  13.  37. 

13.  35.  M- 

13.  38.  o. 

13.  37-  8- 

13.  40.  18. 

13.  49- 


13-     13.      o. 

12.  26-      O. 

13.  38.    30. 


13.  i;.    •). 

13.    39.      i>. 
13.    31.    31. 


13.    37.      O.  12.    40- 


13.    40.      O. 


4t. 
4^. 

7494. 

7558. 

12-     51 

12.  sa 

l.clrc. 

8444. 

I.  13 

i 

8514- 

..  u 

}. 

8575. 

1.  i( 

Finis. 

8694. 

,.  I. 

,.      8. 
.     ft. 

12. 

49. 

5«. 

0. 
0. 

13 

la 

1.   45 

IS. 

53. 

30. 

la 

(.    15- 

■a. 

30. 

|.   51. 

15- 

0. 

J.    17. 

16. 

30. 

}•     2. 

I. 

19. 

0. 

13.    43'    33. 


54-  3>. 

Sft.  II. 

I.    16.  40. 

19.  31. 

I.    30.  45. 

33.  0. 


'■%'         i' 


fft- 


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IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


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us 


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7 


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T, 


Sciences 
Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


92  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Obscn'atio  Eclipseos  Solaris,  Gcdani,  Anno  aerae  Christianae  1652,  die  8  Aprilis  sf,  n.  peracia — Continued. 


O.'ilo  I'has.  '  I'hasium  DlRiti   ^"*' 

CrescSt.           Kcliplici.          I"-' 

uli. 

atio 

lies 
lic- 

\*enim  atcj.  gen- 
uinuin   tein.  ex 
vibrationihiis 
perp.  deductum. 

Tempus  secundfim 
exqiiisitd  sciate 
ricuin    liorizon- 
tale. 

Tempora     secu- 
dftm  liorologi- 
um    ainbiilato 
riura. 

AUitU(lin6s 
C6tri  Solaris. 

,\cciirntum  Temp- 
us  ex    alt.    © 
erutum. 

h.      m.     s. 

gr.    m. 

9096. 

t.      28.      ig. 

I.    29.     0. 

I.   33-     0. 

39-    50. 

I.    29.    22. 

i           .                     9244. 

I-     3>.      45- 

I.    32.     0. 

I.   36.     5- 

39.    32. 

1.    33-   29. 

9454. 

I.      3^.      36. 

I.    37.     0. 

I.   41.     0. 

39.    10. 

I.   38.    19. 

!      10664. 

2.       4.      35. 

2.      5.      0. 

2.      8,   47. 

2.     19.    30. 

2.     23.    20. 

. 

i 

2.    21.      0. 

2.    24.     52. 

2.    25.    47. 

35-    13- 

2.    22         5. 

1) 

461. 

2.      23.      0 

2.    23.      0. 

2.    27.      0. 

35.      3- 

2.    23.    39. 

2.    24.      C. 

2.    28.       0. 
2.    29.      0. 

34-   44. 

2.    25.     14. 

2.    29.      0. 

2.    32.    30. 

34.   37. 
34-   27. 

2.    28.     10. 
2.    29.     16. 

2.    33.      O- 

34.     9- 

2.    32.       0. 

_ 

2.    36.      0, 

4.    48.    15. 
4.    50.    15. 

33-   50. 
17.     4. 
16.   50. 

2.    35.       0. 
4.    45.       9. 

4.   46.    51- 

4.   49-     0. 

4-   53-     0. 

4.   57.     0. 

5.      I.     0. 

5.     3.     0. 

5.     6.   45. 

14.   30. 

5.       3.       4. 

• 

5.     6.     0. 

5.    lo.   20. 

• 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON, 
Animadveriendtt. 


93 


Cum  coeliim.al)  ipso  (liliiculo  iiiatutino,  imbibus  iindiqut'  ifa  csset  olMluctniii,  ut  liiiroloffiiini 
aitificiiile,  tain  .siiijrnla  inimita  se  .iiiiila,  (iiiam  dona  ti'itia  acciiralc  (•oiiiiiioiisIimiis,  lU'fiiie  ad  alti- 
tiuliiK'H  Solait's,  iicqtie  ad  SciattMicuin  diiigi  aKj;    coiiigi  posse,  ul la  spcs  siipeiessi't ;  coiiMiltnm 

esse  diixiiniiti,  hora  statini    lo,  turn  majoiis  fvideiitiiu'  H'litia,  t it  fo  fcitiiis  coiistaivi,  (piot 

eaium  horain  adiiiipU'reiit  intOKiani,  peipeiidiciili  aimotaip  viltrntioiics.  AniiiiiMhcisuiii  auti'in  sii; 
I'uit,  tain  t'x  Sciaterico  iiostro  singula  niiiiiita  inilicaiitc,  afrpiead  liiicani  iiuTidiaiiaiii  lidi-litiT  appli" 
cato,  quaiii  ex  altitudiiiiliUs  Solarilius,  2595  osnillationcs  coiilict'ii'  horaiii  intt'siaai,  &  4314"  iniimtuai 
priiiium  ;  tot  plaue  scilicet,  qiiot  ante  bienninm,  ciica  Eclipsin  Solaiem,in  sirnili  tenipoiis  intervallo 
ejusdeni  perpendiculi  ope  depieliendiinns. 

Jnstante  igitnr  initio  Eclipseos,  praeter  I'eie  ornneni  speni,  Sol  adspectu  mio  nos  exliilaiavit 
adniodnm;  sic  ut  Iioni  11  secnndiiin  llorolof-iuni  anibuiatoriuin,  &  Sciateiicuni,  &  Vibiationes  per- 
pendiculi, exquisite  siniul  conjuKeie  octalq;  coiifei re  liicultas  daretur.  Sole  interim  tuni  teuiporis 
prorsus  existente  puro,  &  A  Luna  illaeso.  Post  initiuin  vero  quod  accnratissitne  anuotatUMi,  Sol 
iternm  sub  nubibus  aliqiiantuliim  lelituit ;  quamquam  postmoduni  i)er  iiitervalla  satis  teniporis 
nobis  consessuni  fuerit  multas  diver sissimasq;  (attestante  observationis  fncoTiisnio)  &  (piideiii  bene- 
ticio  limitatioris  Telescopii,  in  camera  obscurata,  per  iMacliinain,  in  Se!enograi)liia  nostia  p.  98 
descriptam,  ritfe  &  fldeliter  anuotare. 

Quod  autem  in  ipso  Eclipseos  principio  altifudines  Solares  iion  fuerint  a  nobis  eapta,  causa 
hoc  est:  quod  in  tali  Solis  circa  meridiem  situ,  parum  iis  admodum  sit  fidenduni.  Quocirca  alti- 
tudines  circa  exordium  rejecinuis,  usque  dum  Sol  h  meridiano  moveretur  longius;  atque  tuin  denuim 
aliquot  luerunt  notatae,  ad  majoreni  scilicet  observationis  fldem.  Quae  oninei,  ut  cum  sciaterico  & 
perpendiculi  reciprocationibus  quAm  optiine  conveiiiunt;  sic  simul  cum  sciaterico  &  oscillationibus. 
indicant,  in  quantum  horologiuin  nostril  meclianiium,  tam  circa  initium,  quam  tineni.  a  vero  aber- 
raverit  temimre;  ob  quam  tanien  deviationem  l.orologium  islnd  rion  est  plane  conteninendum 
Inde  nauique  verum  atque  exactuin  teinpus,  aeque  ut  ex  sciaterico  &  altitudinilius,  excessu  tantum, 
vel  defectu  probe  atteuto,  elicitur:  imo  denegatis  interdnm,  ob  coelu  subnubiluni,  altitudinibus,  & 
interrupta  adulterataq;  Solis  in  sciaterico  umbra,  ejusmodi  automata  in  observationibuscoelestibus 
summoper^  sunt  necesaaria. 

Caeterum  nolui  omnino  circa  phases  delinendas,  (ut  ut  [)Ierumque  istud  fieri  solet)  non  tantum 
iutegroa  elit;ere  digitos.  semidigitosqne;  sed  quascunq:  designavi,quHe  se  se  commode  ott'erebant 
&  quas  uit6,  &  exquisite  acquirere  me  posse  jiraevidebam,  spretis  reliquis  omnibus.  Qui|)ite  ob 
leve  etiam  impedimeutum,  &  ob  motum  Solis  velocissimum,  haec  vel  ilia  phasis,  licet  maxiaie  eam 
attendamus,  t'acil6  nonnunquam  praeterlal)itur. 

Adhaec  phases  ipsas,  in  adjecta  flgura  I.  aliter  plau(>,  quam  in  Observatione  Anno  1649  habita, 
nimirum  cum  ipais  indinationibus,  nti  in  Tabellft  cameraque  obscurata  sunt  observatae,  onines 
tanieu  sub  uno  eodemque  per|»endicul<),  depinximus. 

Proinde  constat,  Solem  circa  initium  in  77  gradu  it  puncto  Nadir,  ACricain  veraiis,  bora  scilicet 
II. 3'. 21"  fuisse  obscuratum;  atque  circa  25  circiter  gradum  iY  puncto  Zenith,  Aquilonem  versus, 
hora  videlicet  i.ig'.o"  desiisso  obscurari.  Medium  vero,  sive  maxima  obscuratio  liujus  deliquii, 
incidit  circa  phasin  nostrum  16,  hora  scilicet  12.10'  35",  id  quod  pariter  ex  diversissimus  faciebus  in- 
ter se  collatis  satis  certe  patet.  Vera  itaque  ejus  magnitudog^a  digitorum,  sive  9  digit.  &  23'  hie 
Dantisci  esstitit.  liatio  autem  semidiametrorum  Solis  &  Lumie  inventa  fuit  hac  vice,  ut  1000  ad 
1033  circit. 

Quomodo  praetereil  in  Eclipseos  progrcssu  phasium  cornua  se  se  praebuerint  conspicienda,  & 
quern  limbi  gradum  in  omni  positu  tetigerint,  ipsum  Schema  deliquii  cuique  baud  cnrrente  oculo 
id  perlustraturo,  sufflcieuter  o8teu<let.  Quo  verb  adhuc  clariiis  banc  Eclipsin  ponerem  ob  oculos, 
operae  duxi  precium,  pruecipuaa  etiam  phases,  tam  crescentcs,  quilm  decrescentes,  cumearum  incli- 
iiationibus,  ex  majore  Schemate  deductaa,  &  ad  iutegroa  digitoa  propurtionatas,  in  forma  represeu- 
tare  ininori ;  id  quod  nemini  forsitam  accidet  ingratum. 

No  iiltitudeH  having  been  observed  until  the  eclipse  was  entirely  over,  tliere  is 
necessarily  some  little  doubt  respecting  the  correction  to  the  pendulum  and  the  sun- 


^- 


94 


RESEARCHSS  ON  THE  MOTION  OF  THE  MOON. 


dial.  Recomputing  some  of  tlie  altitudes,  I  find  hour-angles  averaging  25*  greater 
than  those  of  Hevelius.  The  corrections  to  the  dial  derived  from  the  first  altitudes 
are  decidedly  positive,  while  the  later  ones  do  not  indicate  any  correction.  The  gen- 
eral result  agrees  with  the  observations  of,  1645  in  indicating  a  positive  correction  to 
the  apparent  time  of  the  sun-dial,  a  correction  which  we  may  estimate  at-|-2  5"dt:  10". 
The  equation  of  time  being -f-i'"  37",  the  entire  correction  to  reduce  to  local  mean 
time  will  be  -fa"  2".  This  correction  is  to  be  a|)plied  to  the  n)ean  of  the  results,  "ex 
vibrationibus  perpendiculi",  and  "secundum  sciatericum". 

I'affo  35. — Eclipse  of  1654,  Aitgunt  12th. 

The  times  do  not  seem  entirely  reliable  unless  they  are  founded  on  more  data 
than  are  given.  The  clock  seems  to  have  been  corrected  by  a  single  altitude  of  the 
sun.  The  following  are  all  the  results  it  seems  worth  while  to  use.  The  second  column 
is  headed  "Horolog.  artificiale  ex  altit.  per2)ed.  correctum"';  the  third,  " Vibi'ationes 
perpendiculi " : — 


H. 

M. 

y. 

8. 

0. 

0. 

0. 

8. 

19. 

3. 

743. 

9- 

0. 

0. 

2340. 

Initium. 

<)■ 

25- 

15- 

3322. 

i-Dig. 

Q- 

26. 

30. 

3371- 

I.  Dig. 

9- 

31. 

0. 

3548. 

2i.&paul6p1us, 

9. 

41. 

40. 

3964. 

3. fero. 

9- 

42- 

58. 

4015. 

3i.  fcr6. 
3l. 

9- 
9. 
9- 

46. 
47. 

48. 

45- 

8. 

22. 

4162. 
41:8. 
4227. 

(  0  cent.  alt. =42°.  53'.  0 
i  0  azimuth  =46°.  18'.; 

'. ;  <  =  9'i.  47"".  8«. 
/  =  9'>.  47™.  3". 

4- 

9. 

49- 

0. 

4289. 

The  times  in  the  second  column  are  deduced  from  the  "vibrationes  perpendiculi" 
in  the  last  by  assuming  39  vib.  =  i  min.,  and  correcting  the  count  by  the  altitude.  But 
in  the  last  there  is  an  en-or  either  of  one  minute  f)r  of  forty  vibrations:  it  h  hard  to  tell 
which.  I  deduce  the  apparent  time,  g*"  46"  55',  from  the  altitude,  13'  less  than  that  of 
Hevelius.  .         . 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  nlj 

Page  45. — Observatio  Edipseog  Solaris.     Gedani.    Anno  1656,  die  26  Januar.  hubita. 


!  Quantitas 
Phasiuin 
observat. 

Oscilla- 
>   tioncs 
pcrpen- 
diculi. 

1     Tempus  ex        ^Ititudines 
Oscillationibus  C^'"'"  ^"'""^ 

erutur  .       P"'"^'  A'"""' 
:        captae. 

Azimulha 

© 
Occident. 

'I'cnipus  ex 
Altitudinibus 
©  supi)utatuin 

0— 

Tempus  ex 

Aziniuthis  de- 

ductum. 

Tempus       ' 
secundfi  horo- 

logium 
anibulatorium. 

0 

0 

h.      m.     s. 

h.      m.      s. 

h.      m.     s.   i 

• 

. 

• 

. 

16.     57.    15. 

0.      0. 

12.      0.      0. 

12.      0.      0. 

12.      0.      0. 

• 

• 

• 

15.    27.    15. 

16.     56. 

1    I.    10.    12. 

I.      9.      0. 

I.      9.    10. 

• 

0. 

I 

30. 

0. 

. 

. 

. 

I.    30.      0. 

• 

587. 

I 

44. 

55- 

. 

. 

. 

. 

I.    45.       0.    ' 

Inilium. 

827. 

I 

51- 

2. 

. 

. 

. 

• 

I.     51.     12. 

^i-  dig. 

1000. 

I. 

55- 

25. 

. 

. 

. 

I.    55.    35- 

H. 

1096. 

I. 

57- 

22. 

. 

. 

. 

. 

I.    57.    32- 

I. 

1170. 

I. 

59- 

50. 

• 

2.       0.       0. 

li.  fe'fe. 

1282. 

2. 

2. 

33- 

. 

2.        2.     49. 

ij.  fer6. 

1495- 

'■ 

8. 

0. 

. 

2.        7.     45. 

• 

1639. 

2. 

II. 

40. 

II.    46.      0. 

3r.    34- 

2.    12.      0. 

2.     II.    22. 

2.     II.     29. 

2i. 

1745. 

2. 

14. 

22. 

II.    33.      0. 

32.    17. 

2.    14.    42. 

2.    14.      0. 

2.     14.      18. 

Paul6  plus. 

1811. 

2. 

16. 

3- 

. 

. 

2.     15.     54. 

3.  dig. 

i860. 

2. 

17. 

17. 

. 

2.     16.     56. 

. 

1961. 

2. 

19. 

51. 

II.       8.      0. 

33.    33- 

2.    19.    48. 

2.     19.    45. 

2.     19.     46. 

3i. 

2029. 

2. 

21. 

35. 

. 

. 

2.     21,     29. 

3?. 

2110. 

2. 

23. 

49. 

. 

2.     23.     32. 

4. 

2213. 

2. 

26. 

16. 

10.    37.    30. 

35.      0. 

2.    26.    21. 

2.    26.     10. 

2.     26.     15. 

4i. 

2302. 

2. 

28. 

31. 

2.     28.     34. 

• 

2400. 

2. 

3'. 

I. 

10.     13.      0. 

36.      7. 

2.    31.      7. 

2.     31.       8. 

2.     31.        5- 

4i.&pau.( 
16  ampl.) 

2478. 

2. 

33- 

0. 

10.      4.      0. 

36.    28. 

2.    32.    50- 

2.     32.     42. 

2.     32.     58. 

5- 

2589. 

2. 

35- 

49. 

. 

. 

2.     35.     59- 

_ 

2595- 

2. 

36 

0. 

9.    48.      0. 

3".     12. 

2.    35-     54. 

2.      35.      58. 

2.    3fi-      3- 

5*. 

2676. 

2. 

38. 

2. 

9.    36.      0. 

37-    3f>. 

2.    33.     10. 

2.    37.    47- 

2.     38.        5. 

•      53. 

2766. 

2. 

40. 

20. 

•     i 

. 

. 

2.     40.     24. 

2814. 

2. 

41. 

33- 

9.    20.      0. 

38.    24. 

2.    41.     15. 

2.     41.      21. 

2.     41.     38. 

5«. 

2820. 

2. 

41- 

42. 

•         •         •     1 

2.     41.     49. 

. 

2898. 

2. 

43- 

40. 

9-       7.    30. 

38.     54. 

2.    43-    32. 

2.    43.    37- 

2.     43.     50. 

6. 

3004. 

2. 

46. 

22. 

8.     52.    30. 

39-    31. 

2.    46.     14. 

2.     46.      24. 

2.     46.     35. 

bi. 

3325. 

2. 

54- 

33. 

8.      8.      0. 

41.     l8. 

2.    54.     19. 

2.     54-     32. 

2.     54.     58. 

6». 

3469. 

2. 

58. 

7- 

7-    47.    30. 

42.      6. 

2.    57-     53- 

2.      5S.      II. 

2.     58.     38. 

6J. 

3598. 

3. 

I. 

28. 

7.    28.      0. 

42.    39- 

3-      0.    25. 

3.      0.    45. 

3.       I.     53- 

7.  frert. 

37". 

3- 

4. 

21. 

;.    12.      0. 

43-    23. 

3.      4.      (>■ 

3.      4-      6. 

3-      4.    41. 

• 

39'3- 

3. 

9- 

29. 

6.    42.      0. 

44.     30. 

3-      9-      5. 

3-      9-     if>. 

3.       9-     51. 

7.&  pau-i 
16  minus.) 

4055. 

3- 

13. 

6. 

6.     IS.      0. 

45-     '8. 

3-     13.       t. 

3-     13.      I. 

3-    13.    4°. 

6H. 

4077. 

3. 

13. 

30. 

J 

. 

3.      14-     12. 

6J. 

4578. 

3- 

16. 

23. 

5-     59-      o. 

46.      0. 

3      16.      6. 

3.     i6-     17-   ' 

3.   16.  46. 

6J. 

4734- 

3- 

20. 

21. 

5-    33-      0.   ^ 

46.    49. 

3.    20.     16. 

3.    20.      8. 

3.   20.   43. 

5136. 

3. 

30- 

35- 

•     i 
i 

1 

3.    3t.      0. 

HEVELurs  states  that 
tion  of  time  is  + '  3'"  20', 
times  in  the  third  column. 


his  pendiihim  made  2360  vibrations  in  an  hour.     The  eqna- 

and  tliis  lias  been  taken  as  the  correction  ajiplicable  to  the 

liut,  as  scarcely  more  than  half  the  eclipse  was  observed, 


96 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


there  is  no  way  of  eliminating  tlie  systematic  errors  of  observation.     Tlie  observations 
are  therefore  of  no  great  valne. 

Page  49  —Occultutio  Stellulae  in  Ariete. 

Anno  1656,  (lie,  9  ,  i  Martii  vcspcri,  diias  Stt'llnlas,  scd  glolm  liactiMins  iiondnm  adscriptavS  i\ 
Lima  pIus()Mani  linnata  ti'i',ta.s  olt.si'ivavi ;  prior  a  supra  ednctioncin  (iaiidac  Aiictis  .sita  est,  ad  17' 
vcl  18'  Hon-ani  vtTSii.s;  n  in  longitudint' vero  ad  n'  |)i'oinotioi'  est,  (piaui  dicta  Stflla  cognita. 
Tt^gebatiir  autein  a  Luna,  alto  Palilicio  38°  13'  30". 

The  mean  time  dedncible  from  this  aUitude  is 8''  34™  45' 

Greenwich  time 7''  20'"    9". 

Page  89. — Obnervatio  Occultationis  Binarum  Stellularum  in  8   1658  Oct.  14.  venperi. 

Stella  una  fuit  aequens  duarum  Australior  in  Collo  8  ,  euJuN  longitntlo  1°  18'  n.  Latitudo  B. 
0°  46'.  Stella  altera  non  hahetur  in  Catalogo  aut  globis:  Krat  auteni  pauloOrientalior  priorc  & 
Borealior,  quain  rursivs  sequebantur  duae  aliae  Slellae,  tanto  intervallo,  ut  omnes  HJmul  Tubo 
(•aperentur. 


Teni 
Horo 

pus 

iuxta. 
m.ajus. 

Alt.  C.a- 
pella. 

Tem 

JUS  ex 
tud. 

Alli- 

9- 

23 

.(6. 

34. 

45. 

9- 

25. 

43. 

g- 

37 

10. 

36. 

=  5. 

')■ 

3Q- 

4- 

Hinc  propter  inlcrvenicntes  nuhes  &  pluvias  Luna  &  Ingressus  Stellae 
sub  Lunani  videri  non  potiiit. 

10. 

S 
5 

0. 
.5. 

■4I)- 

• 

2S. 

II. 

If). 

23. 

Stella  incognita  paulii  minus  disiahat  a  Luna  diametro  Lunari :  & 
pauli)  plus  ((ua  du;u;  Stellulae  eandeni  sequentes  il  so  invlce. 

II . 

20 

0. 

• 

11. 

21. 

15- 

Ingressa  videbatur  Stella  discum  Lunarem  supra  Monti"!  Alabastr. 

• 

• 

• 

• 

Stella  Incognita  non  amplius  conspicua,  videbatur  subiissc  discum 
Lunarem. 

Tlie  following  are  the  mean  times  actually  resnlting  from  the  three  altitudes  of 
Capella,  together  with  the  corrections  to  the  apparent  times  of  Hevelius,  and  the 
computed  clock-corrections :  — 


Mean  Times. 

Dlff.  from 
Hkvelius. 

Clock-cor- 
rection. 

A 

m     s 

m      s 

m       s 

9 

II     34 

-   14     14 

~   12     12 

9 

24     50 

-   14     i-l 

—   12     20 

ti 

I     39 

-   14     58 

-   13     36 

The  equation  of  time  is  actually  14™  3".  The  first  two  altitudes  agree  well  enough 
with  this.  But,  in  the  case  of  the  last,  there  is  clearly  an  error  of  about  ten  minutes 
in  printing  the  clock-time:  it  may  be  assumed  that  th'e  minutes  should  be  15  instead 
of  5.  But  there  is  still  a  discrepancy  of  more  than  a  minute  between  the  correction 
from  this  and  from  the  firsi  two  altitudes.  A  change  of  5'  in  the  altitude  will  reduce  the 
difference  from  IlEVELurs  to  14'"  23",  and  the  clock-correction  to  13™  i".  The  mean 
of  this,  and  of  that  computed  from  the  altitude  as  given,  is  13""  18",  winch  I  shall  accept 
as  the  most  probable  result  of  tlie  altitude.     The  first  two  altitudes  give  a  result  i"  less. 


RliSEARCUKS  ON  Tlir-:  MOTION  OF   lUK  MOON.  y7 

Notwitlistivnding  the  lapse  of  two  hours,  I  cciiisidor  tlioiu  entitled  to  some  little  wei<^ht 
in  the  result,  .and  shall,  therefore,  adopt  the  dock-correction  13'"  5",  which  gives  ior 
the  time  of  occultation  1 1''  6'"  55". 

The  probable  error  of  clock-correction  may  be  estimated  at  30",  and  that  ot 
the  observed  clock-time  at  15".     We  then  have,  for  the  fJreenwich  mean  time  of  the 

occultation, 

c/  52'"    1 9"  ±3  5". 

To  this  probable  ei-ror  (jf  time  is  to  be  .added  the  uncertainty  whether  the  actual 
occultation  was  re.ally  seen,  as  it  must  have  taken  place  at  the  bright  limb. 

Page  2i'j.—Occul(atio  Clarae  Boreal  infronte  Scorpii,  1660,  27  Apr.  mnm': 


li      in 

ITorolog.  I.  32.  57.    Alt.  Spiea 


I.  49.  35.      "     Arctnri      47.  58.  o. 


16.  43.  o.     Toinp.  ex  altitii.  i.  38.  15. 


I.  50.  10. 


47.  52.  o. 


I-  54-  3- 

I-  54-  S^"- 

2.  39.  o. 

3-  35-  34- 

3-  42.  7- 

3.  44.  6. 


2.  34.  30.  Exitiis  Sk'Ua.  Optiine  coiisiK-xiinus. 
3'  30-  30'  Alt.  Ar(;t.  34.42.0. 

3.  36.  15.  33-    46.  o. 
3.  38.  3S.  33-  29-  °- 

The  clock-corrections  resulting-  from  these  altitmles  are: — 

(i)-f4"-42» 
•        ,  .  (2)-f  3'"3i" 

(3)  +  3'"4«" 
(4) +  3"  50' 
(5) +  4™  36" 

■    •■  (6)-^ri5". 

The  resulting  mean  (dock-correction  is  +  j['"  7^  and  the  probable  error  of  both 
clocks  and  observ.ations  al)out  8".  T\w  Cireenwich  mean  time  of  the  occultation  is 
therefore  13''  24'"  i»  ±  i2». 

Page  23S.—Occultatio  Spieae  Vir<jini:i,  1660.  die  Jovis,  17  Juni.  vesp. 


Altitudiues.     Tempus  ex  altitud. 
o       /         //         O       I       II 


Horolog. 
/(.    m.   s. 

9.  51.  10.  Arcturi  .    .    51.  38.    o.      9.  53.  10. 

9.  56.  15.  Spicao    .    .     18.    2.    o.      9.  59.  29. 

10.    o.    o.  Marg.  d  Slip.  18.    8.    o.     10.    2.  15. 

•o-  33-  35-  Arcturi  .     .    47.     5.    o.     lo.  36.  10. 

10.  37.  20.  Marg.  d.Hup.  14-    o-    o.     10.  39.  30. 

lObtegebiUur  Spiea,  "J^  a  Luna 
:o.  54.    o.  10.36.    O.J     circa  parte  sc.  obscnrau). 

11.  32.  20.  Arcturi  .     .     39-  45-     o-     "•  33-    33- 

,j    --    ,0,  II.  41.  30.     AdliucpostLunainlatebat  Spica. 


1.}- 


-75  A  p.  2 


9» 


RF.SEARCIIES  ON  THE  MOTION  OF  THE  MOOiV. 


Animadverlenda, 

rostinotliim  uiibes  Lunaiu  coelumque  tegebaut,  ut  iiiLil  amitliusdeexitu  Siticaeileiirelieiideie 
potuerimus. 

Tlie  following  are  the  results  of  the  altitmles  of  stars: — 


Cloc 

kT 

mes. 

Compii 
Mean  Ti 

ted 
mes. 

Diff.  from 
Hevee.ius. 

Clock-cor- 
reclion. 

m      i 

A 

tit 

s 

A 

m 

s 

m 

s 

9 

51 

lO 

') 

53 

21 

+  0 

11 

+    2      II 

0 

56 

•5 

9 

59 

57 

+  0 

2S 

•f    3    42 

10 

33 

35 

lo 

36 

19 

+  0 

9 

+  2    44 

II 

32 

20 

II 

33 

41 

+  0 

8 

+  I     21 

The  mean  of  the  four  clock-corrections  is  +2"'  30'  ±  12".  Hut  the  small  cor- 
rection resulting  from  the  last  altitude  gives  rise  to  at  least  a  suspicion  of  a  large  clock- 
rate.  The  rate  deduced  from  the  observations  hy  least  squares  is  —  o"  88  per  minute, 
and  the  correction  at  the  time  of  occultation  will  become  -f  2'"  7'.  But  the  existence 
of  so  large  a  rate  seems  quite  improbable.  I  shall  therefore  adopt  -f  2'"  25*  ±  13"  as 
the  most  probable  correction-  at  the  moment  of  occultation.  This  will  give  for  the 
local  mean  time  10'' 56"  25",  and  ; 

9''  4i'"49''±  20»     ; 
as  the  probable  Greenwich  time  of  the  occultation.  '  '; 


RESEARCHES  ON  THE  MOTION  OF  THE  MOoN. 
Page  301. — Eeliimit  Solaris,  Anno  iCoi,  die  30.  Murtii. 


99 


Quanlil.is 
Pliasium  Obscr- 

Horolog 

um 

Horoloj; 

uni 

A 

tiliidines 

TeiTipus 

Anlmadventcnd.T. 

vala. 

Amb 

ulatorium. 

perpendiculi. 

-Solis. 

concclum. 

Amb.  Clock  Corr.  M.  T. 

0- 

I. 

21. 

9- 

I  . 

1 

1 

21.    1 

23. 

23- 

0. 

9- 

3-       9- 

+  7'"-     .5"- 

• 

9- 

2. 

35- 

9- 

2. 

36.    1 

23. 

3i. 

0 

9- 

4-     54- 

7         43 

•• 

9- 

JO. 

29. 

9- 

10. 

10.    j 

29. 

29. 

0 

■ 

9- 

.2.     53. 

dub.        7         49 

• 

9- 

45. 

35- 

9- 

45- 

'3-    1 

33- 

0. 

0 

9- 

47-      23. 

+   7           2 

Initium. 

10. 

12. 

3- 

10. 

II. 

41-  ! 

.0. 

13-     15- 

Initium  circa  117°  1l  puncto  Zeuilli  con- 

l.Uig. 

10. 

IS- 

25- 

10. 

13- 

5-    1 

10. 

14-     37- 

ligit. 

». 

10. 

IS- 

63- 

10. 

13- 

33- 

10. 

15-       4- 

0  • 

10. 

15- 

42. 

10. 

.5- 

24- 

10. 

16.      56. 

^ 

10. 

17. 

8. 

10. 

16. 

sa- 

10. 

18.      22. 

I  d.&  amplius. 

10. 

18. 

31. 

.0. 

18. 

ls- 

10. 

19.     44- 

li.feri. 

10. 

20. 

15- 

10. 

10- 

58- 

10. 

21..    27. 

Ji. 

10. 

23- 

>7- 

10. 

23- 

0. 

10. 

24.    27. 

3h 

10. 

34- 

24. 

10. 

34- 

10. 

10. 

35.     3'- 

4h 

10. 

43- 

... 

.0. 

43- 

5- 

10. 

44-      20. 

■     5». 

10. 

5'- 

53- 

10. 

51- 

43- 

.0. 

52-      53- 

5;. 

10. 

52- 

49- 

10. 

52- 

45. 

.0. 

53-      54- 

6  d.  &  amp. 

10. 

54- 

36. 

.0. 

54. 

31- 

10. 

55-     40- 

l*ortio  circlili  I.unarib  per  centrum  Solis 

61. 

7.circiter. 

10. 
10. 
II. 

55- 

57- 

1 . 

31- 
26. 

56- 

10. 
10. 
II. 

55. 

57- 

I . 

26. 
23- 

55- 

10. 
10. 
11 : 

Sfi-      34- 

53.      29. 

3.       0. 

transiens,  vel  obscurata  pars   Sdlis, 
hora    10.    55'    contineliat    in    Limbo  i 
Solari  wa". 

1 

7.paul6  plus. 

II. 

5- 

6. 

II. 

5- 

0. 

... 

(,.       4- 

Ratio  Diametri  ©  ail  Dianict.  C  •  obser-  ' 

7i.circi. 

II . 

6. 

19- 

II. 

6. 

15 

... 

7-     17- 

vat,  est  ut  1000  ail  1105.    Data  if^itiir 

75. 
7i. 

... 
... 

.2. 
.4- 

10. 
15- 

... 
... 

.2. 
14- 

It. 
14- 

... 
II. 

>3-       8 

I;.          9. 

scmid.  0  ex  meis  observatis  15'  54" 
provenit  scmid.    D    in    hac    Kclipsis 

16'J4".                                                                       1 

7i. 

.1. 

33- 

44- 

... 

33- 

4.. 

... 

34-     34- 

Max.  obsc.  II.  JO. 

e^.feri. 

.1. 

46. 

54- 

... 

56- 

50. 

4j.fer6. 

... 

57. 

47- 

... 

57. 

45- 

45. 

I.. 

59- 

36. 

... 

59 

31- 

■ 

3i. 

.2. 

.. 

20. 

.2. 

.. 

19- 

. 

al. 

12. 

8. 

25- 

.2, 

8. 

20. 

. 

28. 

.2. 

9- 

32- 

.2. 

9- 

28. 

. 

ai.fer  . 

.2. 

... 

0. 

.2. 

... 

0. 

• 

»i. 

.2. 

12. 

15- 

12. 

.2. 

15- 

, 

« 

»t. 

12. 

13- 

0. 

2.paul6  plus. 

12. 

13- 

45- 

12. 

13- 

45- 

. 

li.feri. 

.2. 

15- 

15- 

12. 

15- 

15- 

»i- 

12. 

If). 

.0. 

12. 

.f). 

10. 

. 

l«. 

12. 

17- 

0. 

12. 

.7. 

0. 

, 

, 

it.feri. 

12. 

IS. 

20. 

12. 

18. 

17- 

* 

. 

ih 

.2. 

"9- 

20. 

.2. 

19. 

19- 

. 

iS. 

.2, 

19. 

57- 

12. 

iq. 

57- 

I.  fere. 

.2. 

2.. 

9- 

.2. 

21. 

9- 

i. 

12. 

22. 

8. 

12. 

22. 

8. 

. 

1. 

.2. 

23- 

34- 

12. 

■•3- 

34- 

. 

1      ■ 

. 

39- 

21. 

40. 

.2 

26.     17. 

Finis. 

12. 

26. 

39- 

12. 

26. 

40. 

. 

.2. 

27-        3- 

Finis  circa  81°  4  puncto  Zenith,  occidit. 

. 

.2. 

51- 

55- 

dub. 

3S. 

33- 

20. 

.2 

51.      46. 

+   2'       2"        +   6     .8 

. 

.2. 

57. 

49- 

. 

38. 

.6. 

35. 

12 

58.       6. 

.57               6     39 

. 

.2. 

58. 

49. 

38. 

13- 

25- 

.2 

59-      14- 

.52               6     42 

.    I. 

0. 

35- 

• 

• 

• 

38. 

7- 

30. 

I 

I.      17. 

•      47               6     54- 

100 


Ur.SEAUCllF.S  ()\  THK  MOTION  Ol'  TIIK  MOON'. 


AnimaHferteHtln. 

Inatunte  liao  Eclii)si  8olis,  oimu'in  ad  liibuiinus  operain,  ut  cum  loiigJ)  ex  optatissimo  nostro 
liospito  J)ri  Ismacli  BuUialdo,  oinniii  ilia,  iiiiao  ad  oclipsiri  oliscrvaiidam  spectaie  arbitrabar,  esseiit 
ill  promtii;  itiipriimia,  diias  oamcviis  obsciirataM  adornavi,  altoraiii  pro  Miijoribiis,  alteram  pro 
Miiioribiis,  qui  iu  magna  aderant  frequcutia,  et  (juidem  en  ralione,  qua  videbautur  commclloref. 
Multo  mane,  die  30  Martii,  orieiite  Hole,  qiianiqaam  CoeUini  undiquo  erat  sercuum,  sub  lioram  tameu 
oetavani  nubibus  satia  obscuris  obduei  coepit,  adeo  ut  Solem  Qiiadrante,  nee  JIajori,  nee  Minori 
iiostro  aenco  rimari  potuerlinus.  llora  verb  9,  ai-r  pabuliuu  attenuabatur,  ut  satis  accurate  alti- 
tudiues  Solares  caperentur ;  quo  tempore  Ilorologium  tam  perpendiculare,  quam  asitatum  ambu- 
latorium,  una  cum  Seiaterieo  iu  ininutis  distributo,  i)raeei.si!  admodum  conveniebat. 

llora  9.  30',  Camerani  iiigressi  siimns  oculos  delixos  oniniuo  iu  Tabula  observatoria,  praesenti" 
bus  praecipuis  Nostrac  Urbis  Luuiinibus,  tenentes,  nc  nobis  initium,  quod  iustare  judicabam,  ela- 
beretur.  lluic  nostro  proposito  Coelum  tum  claia  etiam  facie  aunuit,  sic  ut  ipsum  Lunae  sub  Solem 
ingressum,  punctuinquo  attaetns  dilmiide  admodum  eonspiceretur,  in  117°  a  puncto  verticali, 
occasum  vert-iis;  &  quidem  primiini  a  Praeelarissimo  BuUialdo  minimeotiosum  se  praebente  specta- 
torem. 

•  •  •  •  Semidiamelrum  Lunae  notabiliter  uiinorem  esse,  in  boc  deliquio,  qutYm  quidem 
Calculus  proraiserat;  quae  iu  peculiari  cbarta,  ex  tribus  in  periplieria  Lunae,  i\  tribus  diversis  obser- 
vrttionibus,  simul  notatis  panctis,  multoties  explorata  est. 

•  •  *  pbasiu  tamen  istam  maximam  aeeurato  obtinuiraus:  73^  digit,  iiempi-  Imud  fidase 
uiajorem.    •    •    *. 

Hora  12  26'  17"  alto  Sole  39°  21'  40".  (Juadrante  Azimulliali  uostro.  in  altera  satiy  longe 
dissita  specula  nostra  coustituto,  alias  Obscrvator,  liarum  rerum  alias  bene  gnarus,  (iuem  Eclipsis 
in  pinnacidio  Quudrantis,  per  nudum  foramen  depreliendit. 

Quod  etsi  cum  uostro,  ojte  Teleseopii,  in  Gameril  obscarata,  annotato  fine,  in  upsis  secundis 
non  conveniat  (nee  sane  adeo  occurale  ista  rations  unquam  fieri  potest.)  tameu  lubens  etiam  banc 
Observatiouem  api)oner«  volui;  <iub  videas  in  ista  minus  acciuata  observatione,  non  nisi  46"  aberra- 
tum  esse:  quod  profectb  nullius  est  momeuti,    •     *     •     •. 

Rejecting  the  altitiules  within  half  an  liour  of  noon,  the  eight  otliers  give  the  fol- 
lovvino-  clock-corrections : — 


Hor.  amb. 

Corr.  to 
Hor.  amb. 

Corr.  to 
Uor.  pcrp. 

/i      m 

s 

m 

s 

m      s 

')   I 

2t 

+   7 

15 

+  7  «5 

2 

35 

7 

43 

7  42 

10 

20 

7 

49 

7  63 

"(S 

35 

7 

2 

7  24 

12  51 

55 

+  6 

:3 

57 

49 

f> 

39 

58 

49 

6 

42 

•   60 

35 

0 

54 

Taking  the  means,  we  have : — 

At    9''.25,  corr.  Uor.  amb.  +  z"  27";  corr.  Hor.  p.  +  7'"  38". 
At  I2^93,  corr.  Hor.  amb.  +  6'°  38";  corr.  Hor.  p.  +  6™  38'.  (?) 

These  corrections  being  interpolated  to  the  times  of  observation,  the  mean  result 
from  the  two  clocks  i,s  taken  as  the  local  mean  time. 


RESEARCnr.S  ON  TllF,  MOTION  Ol'  Tin:  MOON.  101 

^  I'ngo  330. — Ovcultalio  tSaiitrni,  iCCi.  ;i  Avguad  Vesj).  si.  n. 
'Jliero  is  only  ii  single  colnnin  of  times,  wliieli  is  lieadcd  "IVnipus  ex  liorolog; 
rtostimat  siniul   coiTOctuni".      [  am    tlierofoio  in    doubt  how  tlio   observations  ■wore 
inado,     Hie  following  extracts  are  all  tliat  ean  lie  of  any  nso: — 
Teinpiis  ex  Sec: — 

7.  58.    o.     h  Liiiil).  J  striiigcbat. 

7.  58.  20.    Vcrum  iuitiam  occult.    Hubivitdiiiiidio  copore  qimiitmii  conjicoic  liciiit. 

7.  59.  50.    Tertiii  pars  ndhiic  vidcri  potiiit. 

8.  o.  25,    Sutiu'inis  totus  occiiltat. 

8.  6.30.    Alt.  D  limb.  Slip.  16^  2j' ciic. 
9-    3-  35-    Iiiitltnn  eiDcrsloiii^. 

9.  4.    o.    Jam  luiijor  particula  de  '?  appaniit. 

9.    4.  10.    Finis  occultatioiiis.    Jlediri  'p  corp.  visfi. 
9.    4.  35.    Nondfi  totus  cOspcct. 
9.    4.45.    Finis  totalis  cmcrsioiiis. 

9.  50.  S3.    Altit.  Arcturi      27.  31.  o. 

9.  54.  36.  "  Sclieat  Pcgasi 38.  33.  o. 

•     9-  57-  44-  "  "  "  39-  2°-  °- 

11.    1.36.  "  Scbedir.  Cassiop S3"  i3'  o. 

ir.    7.    7.  "  Capella 17. 56.  o. 

II.    8.  4^-  18,    4.  o. 

II.  II.  3°-  18.  17.  o. 

Uesidea  having  to  take  the  times  entirely  on  credit,  these  observations  are  subject 
to  other  sources  of  doubt.  That  Saturn  should  have  ajjpeared  half-covered,  "quantum 
conjicere  licuit",  twenty  seconds  after  it  touched  the  moon,  wjiile  one  third  was  still 
visible  a  minute  and  a  half  longer,  is  something  ditlicult  to  accept,  even  making  all 
allowance  for  uncertainty  of  oliservation,  and  leads  to  11  susj)icion  of  an  error  of  a 
minute  in  the  second  time. 

Page  419. — OccuUatio  Irium  SMIidarum  in  Capite  Taitri  1663,  14  AJar.  tcspcri.    Stellula 

interior  A  quartao  magnitudiiiis,  cnjiis  longitiido  est  i''  54'  II  &  Lat.  5°  33'  Aiist.    •    *    St.  IJ. 

Austral,  sequentium. 

Tempiis  sec.  boi-.  nmb. 
11.   M.     S. 

8-  53-  3°'    Initium  occultationis,  *  A. 

8.  55.    o.    Altitudo  Arcturi 27°.  3'. 

9-  42.    o-  "  " 34.    12. 

9.  44.    o.    I'riucipium  occultationis,  *  IS. 
9.  47.    o.    luitiuin  occultationis,  *  C, 

9.  52.  30.    Altitudo  Arcturi 35°.  42'. 

The  clock-corrections  given  by  the  three  altitudes  are : — 

(0  +45"  45" 

(2)  +48"     5' 

(3)  +48'"  io\ 

The  clock-corrections  I  .shall  adopt  are,  for  the  first  occultation,  -j- 45™  55';  and, 
for  the  two  others,  -f48"'  7'.  Hie  Greenwich  mean  times  of  the  occultations  will 
then  be: — 

Star  A  (71  Tauri)     .     . 8''  24™  49"  ±40" 

Star  B  ((9i  or  ©a  Taiu'i)      . 9"  17"  3i'rt2  5'' 

Star  C  (©a  or  0,  Tauri)      . 9''  20™  3i'±25». 


102 


RKSEARCIIKS  0.\  THE  MOTION  or  Till-   MOON. 


I'lige  423.— iMi,  Any.  18.     Occiilldtion  of  a  star  during  lunar  ccliiinc. 
Ilorol.  aiiili.  '        ' 

«.   SI.   2«-     Alt.  Alotllli     .     .     .  27.   .s« 

**•  53-  S3-       "        "  ■    .    ■  2 7-  .V) 

9.  II.  36,    Stella. jiun  occiiltntii. 

').  42.  43.    Alt.  liiicidiieCoronnc.  37 

9.  44.  4«-       "         '*  "  37 

9.  46.  36.     J   Ljtiibi  HiiiJorioriH.  i:1 

10.  I.  30.     Stella  nu'siis  prodiit 

11.  14.  37.    Alt.  Lvrae,     .    .    .  58.  37 

1 1.  18.    4 sS-  1' 

1 1.  19.  40 

12.  8.  46 

12,   10.   25 


3'- 
I  2. 

54- 


57-  45- 
SO-  39- 
o.   26. 


.1 


Temp.  iMiir 

«.  S-'.  5-^ 
X-  55-  3 
<).   13.     o, 

43-  3.S 

4S-  45 

47-  3<' 

2, 

'S 
19 


') 

') 

9' 

10. 

1 1, 

1 1. 


12.   II. 


3°- 
1 1. 


11.  21. 

12.  10, 


n- 

3' 
39' 


'lie  ressiilts  of  the  altitudes  of  stars  are : — 


Moan  Tinits. 

Diir.  from 

llKVEI.IliS. 

m    s 

Clock-cor- 
rcclion. 

1      A 

m 

t 

m 

J 

'       8 

55 

40 

+ 

2      48 

4- 

4 

12 

i       8 

57 

50 

+ 

2     47 

+ 

3 

57 

9 

46 

3'5 

+ 

2     55 

+ 

3 

47 

9 

48 

40 

+ 

2     55 

+ 

3 

52 

11 

17 

54 

•4' 

2     43 

+ 

3 

17 

II 

21 

3 

-t- 

2       I 

(  + 

2 

59) 

11 

24 

12 

+ 

2     55 

4- 

4 

32 

12 

13 

8 

+ 

3       5 

+ 

4 

22 

12 

"4 

37 

+ 

2     53 

4- 

4 

12 

The  eqiintion  of  time  was  -|-3'"  15",  so  that  the  ajiparent  times  of  Hkveuus  seoii 
ahout  20"  too  small. 

'i'he  sixth  correction  may  bo  rejected  on  account  of  the  discrepancy  between  the 
altitude  and  the  time  computed  by  IIi:vi:lius.  The  mean  of  all  tlie  other  clock-cor- 
rections is  +4"  r,  and  there  does  not  seem  to  be  any  sensilde.  dock-rate. 

Applying-  this  correction,  we  have : — 

Greenwich  mean  time  of  immersion  of  f'^  Aquarii    .     8''     1'"     i''-j-.r2'' 
Greenwich  mean  time  of  emersion  of  e'^  Aquarii      .     8''  50'"  55'  ±  12" 

I'age  4^)5.— Occ«i<«<('o  PaUlicii,  1664,  die  i  vcup.  31  Marlii,  quarfa  die  post.  6  . 

Toinp.  sec,  hor.  aiiib. 

ir.    M.     S. 

9.  14.  II.    luitium  occult;  Palilicli  A  J. 

9.  17.  30.    Altitudo  Procyonis      .     . 

9.  I      35- 

10.    4.  20.    Finis  occult. 
10.    7.  50.    Altitudo  Procyouis     .    . 
10.    9.  57.  "  ".  .    . 


3I.O    22.' 

0."  Quad.  p.  Or 

31.      10. 

0. 

25,         7, 

0. 

24.      47. 

0. 

rksi:ar(Iii:s  on  tiii;  motion  oi-  tiik  moon,  103 

Tlio  (•lock-coiTcctioiiH  I'l'siiltin;,''  t'nini  the  four  ii]titii<!ts  iiic; — 

(1)  4-  10'"  20' 

(2)  +    9'"  5«' 

(:,)  +  II"'  50"  * 

■   (4)  +  11'"  4.V- 

I  adopt  the  clock-cunt'ctioiis  4- 10'"  9"  lur  iiniiu'sidii,  iind  4-  '  '"'  4^>"  '••'■  I'liicr.Hioii, 
'I'lio  results  ftre: — 


(ireouwlc'Ii  nu'im  tiiiu'  of  iiiniicrsioii 
(rrcc'iuvicli  monn  timo  of  ciiicrsioii 

I'iigo  474. — ikUpHis  SulariH  1666.  2  Julii  maiir. 


S''  c/'  44"  ±  iS- 
9''   1'"  ,iO"  ±  ^S^ 


■  .      - 



1 

~-  

-"  --^ 





— -•  —  - 

Temp. 

1 

Quantilas 
Phasium. 

avstlmatuin 
secundum 
IIi>riilo}j. 

Tt-'hipus 
CornTiuni. 

'» 

A  nib. 

-1 

n.  M.    S. 

Inilinin. 

6.    55.    3"- 

(>. 

57.   y>- 

&^ 

7. 

55-    45. 

'.'.(life'. 

f).    57.    30. 

5'>.    3". 

v„* .  piitito  iniiMi^ 

7- 

59-       5- 

3- 

7.      0.    23. 

2.      23. 

8i. 

8. 

(>.     3». 

8. 

8. 

30. 

li. 

7.      2.    30. 

4.  30. 

7.'. 

8. 

II.    25. 

8. 

'3. 

25. 

Mil-,    si'inid.    S    ail   R" 

ij. 

7.      4.    5<'- 

(1.    50. 

7\.k;i:     •■ 

8. 

17.    30. 

8. 

19. 

30. 

VL'l  i}"  major  ;i|)|)aniii. 

li'.feri'. 

7.     >"•    S7. 

'2.     5?. 

■J.inri:. 

8. 

"9.    41. 

8. 

21 . 

41. 

33- 

7.     M.    5<J- 

If..     59. 

51. 

3. 

28.      8. 

8. 

30. 

8. 

* 

33- 

7.     17.    50. 

I').    50. 

Si.Lti: 

8. 

30.     14. 

S. 

32. 

14. 

4^. 

7.    21-    35- 

23.    35. 

yi- 

8. 

36.     ■.•5. 

8. 

3S. 

25. 

4;i. 

7.    23-    43- 

25.    43. 

3-- 

S. 

43.     19. 

8. 

45. 

'9. 

5i.» 

7-    27-    53- 

29.    53. 

31- 

8. 

41).     12. 

8. 

45. 

12. 

(>. 

7.    3'.    50. 

33.    50. 

3- 

8. 

47-    32. 

S. 

49. 

32. 

63. 

7.    36.    55. 

38.     5.i. 

23. 

8. 

50.    57. 

8. 

52. 

57- 

6|.paulu  plus. 

7.    38.      5. 

40.       5. 

2i.ffic. 

3. 

54.     15. 

8. 

56. 

15. 

7i. 

7-    39-    45. 

41.    45. 

.  ■! 

8. 

SS.    24. 

9. 

0. 

24. 

7}.pauli)  plus. 

7.    42.    30. 

44.     30. 

]  1 

8. 

59.  35. 

9. 

I. 

35. 

7i. 

7.    44.      6. 

46.       f>. 

o\\. 

9- 

I.  33. 

9- 

3. 

38. 

73  • 

7.    46.      0. 

43.      0. 

«;. 

9. 

3 .    20 . 

9. 

5. 

20. 

8.fer6. 

7.    48.    25. 

50.     25. 

Finis. 

9. 

('■     53. 

9. 

8. 

53. 

8^. 
8i.paul6  plus. 

7.    5'.    15. 
7.    53.    37. 

53.    15- 
55-    37- 

0alt. 

. 

©alt. 

47-   33.     0. 

9. 

23.      6. 

9. 

25- 

28. 

17.  45.     0. 

5.     51.     II. 

^. 

53.    12. 

47.    42.      0. 

9- 

24.    16. 

9- 

26. 

45- 

18.  37.     0. 

5.    57.      5- 

5. 

59.     23. 

4S.    10.      0. 

9. 

28.    29. 

9. 

30. 

40. 

18.   55.     0. 

6.      0.      0. 

• 

6. 

r.    23. 

48.    23.      0. 

9. 

30.-    36. 

9. 

33- 

12. 

*Semid.  J  aequalis  cxiitit  Solari. 


104 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Til  '  "notauda"  whii.li  follow  contain  nothing  worthy  of  remark. 
Tho  corrections  to  reduce  the  clock  to  mean  time,  as  given  by  the  individual  alti- 
tudes, are  as  follows : — 


Hor,  amb. 

Corr. 

h 

m 

S 

m     s 

17 

51 

II 

+   5  4S 

17 

57 

5 

6   4 

,S 

0 

0 

5  16 

21 

23 

6 

+  5  53 

21 

2-t 

16 

5  58 

21 

28 

29 

5  36 

21 

30 

36 

5  56 

The  mean  correction  derived  from  the  iirst  group  is  +5™  43",  and  from  the  last 
+  5'"  51".  The  uncertainty  of  the  corrections  is  as  great  as  their  ditference;  we  there- 
fore adopt  the  constant  correction  +5"  47'  ^'*  reduce  tlie  clock  to  mean  time. 

Pago  550. — 1671,  A/«>y;/(  14.     0(ct(U(ttion  0/ lu-o  itarn. 


Hor.  amb.     7.  16.40.  Alt.  ralilidi, 40-3^.    J-    Quad  p.  Or. 

7.  35,  30.  Alt.  iner.  Pollucis,     ....    64.  23.  40     (^iiad  Ax.  M. 

8.  10.  20.  Alt.  Palllicii, 33.  40,    o. 

8.  12.  15.      '•         "  33.  29.    o. 

8.  51.    o.  Stellala  incognita  supra  medium  caudam  T  a  D  corniculalA  tcota. 
8.54.    o.  Media  candib  T  il  Luna  tt'cta. 

Alt.  Palilicii, 27.  29.    o. 

9.  42.    o.  Iiiitium  eniersionis  Mediae  caudae  f. 

9.  57.  40.  Alt.  Humeri  dextri  Orionis,  .    22.  29.    o. 

10.       O.       O,  "  "  "  "  .       22.    12.       O, 

The  following  are  the  results  for  clock-corrections  : — 


Clock  Times. 

,  Mean  Times 
jfrom  Altitudes. 

Clock-cor- 
rection. 

C. 

/t     m 

s 

//  m      s 

m 

s 

;«  s 

1     16 

40 

7  27  47 

+  II 

7 

+ 

II   0 

8  10 

20 

8  21  58 

+  II 

33 

+ 

II  53 

8  12 

15 

'   8  23  18 

•h  II 

3 

+ 

II  55 

8  54 

0 

9   f'   9 

+  12 

9 

+ 

12  37 

9  57 

40 

1  :o  12  14 

+  M 

34 

+ 

13  41 

10   0 

0 

,  10  14  17 

+  14 

17 

+ 

13  43 

The  clock-corrections  are  quite  uncertain,  owing  to  uncertainty  whether  the  differ- 
ence of  throe  mituxtes  between  the  clock-correction  given  by  Aldebaran  and  that 
given  by  «  Orionis  is  the  result  of  clock-rate,  or  of  systematic  error  in  the  observations 
of  one  of  the  stars.     If  we  suppose  a  rate  of  one  minute  per  hour,  the  mean  correction 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


los 


will  be  as  in  the  last  column.     I  shall  adopt  this  correction  as  on  the  whole  the  most 
[)robable.     The  results  arc: — 


Greenwich  mean  time  of  immersion  of  star 
Greeiiwich  mean  time  of  immersion  of  star 
Greenwich  mean  time  of  emersion  of  star 


7"  48"  5^^  ±  2  5" 
I"  it  25' 


7"  52" 


8"  40™  49"  ±  40'. 


I  have  not  succeeded  in  identifying  these  stars.  The  descriptions  would  seem  to 
refer  to  S  and  5  Arietis,  but  neither  of  them  were  near  ihe  computed  position  of  the 
moon's  limb  at  this  time. 


Ooeultatio 

Spica  Virf/iim,  1671,  22  Aprilis. 

H.    M.    S. 

Ilorol.  Ami) 

9-  S-'-  45- 

Altitiulo  PoUucis     .     .    .     • 

35- 

27- 

0. 

9.  55.  20. 

"             "           .... 

35- 

8. 

0. 

JO-  45-  35- 

Initiiim  Oectiltatiouis.  .    .     . 

•■•  '5-     5- 

Alt.  B  limb,  infer 

25' 

50- 

0. 

1 1.  54.     0. 

Spica  iieediim  conspecta. 

II.  55.     0. 

Aillinc  (It  bitescebat. 

"•  55-  30- 

Spica  emersit.    Finis  occult. 

12.     0.  39. 

Alt.  Kog 

26. 

18. 

0. 

12.      2.     c;. 

ii        a 

26. 

3- 

0. 

J  2-  36-  55- 

Alt.  Lyrae 

49. 

39- 

0. 

12.   3<).  23. 

U            l( 

49. 

5°- 

0. 

Temp.  (-'oil. 


II.  M.  H. 

9.  56.  21. 

9.  58.  32. 

10.  47.  56. 

11.  17.  25. 


11.  57.  10. 

12.  2.  14. 
12.  4.  O. 

12.  39-  45- 

12.  41.  o. 


Hevei.iu.s  <>iv('s  altitude  of  Regulus  36.  18.  o.  at  the  moment  of  immersion;  also, 
"Emersionsis  ►Stollao  aecuratissime  deprehensum  est".  Tlie  mean  times  computed  from 
the  altitudes  compare  with  those  of  Heveluts  as  follows: — 


Mean  Times. 

Diir.  from 

IIliVELlUS. 

Clock-cor- 
rcclion. 

/* 

m 

s 

m    s 

Ill 

s 

9 

54 

52 

—   I     29 

\-  2 

7 

y 

57 

30 

—   I       2 

+  2 

10 

10 

46 

42 

-   1     14: 

+   I 

9 

12 

1 

9 

-    I       5 

+  0 

30 

12 

2 

55 

-   I       5 

+  0 

46 

12 

3S 

21 

-   I     24 

+    I 

26 

12 

39 

37 

-    I     23 

+  0 

14 

Tlie  mean  result  is  that  at  ii""  26™  the  dock-correction  was  4-  1™  12".     I  shall 
admit  a  rate  of  —  24  seconds  per  hour.     The  results  will  then  be : — 

Greenwich  mean  time  of  innnersion 9'' 32"' 25"  ±  15' 

Greenwich  mean  time  of  emersion       10'' 41"  54"  ±  15'- 

Page  564.— Occultation  of  Satiun,  167 1.  June  1.  mane.    Tlie  times  are  so  discordant  that 
the  observations  seem  worthless.    IFere  'lowever,  are  tlio  observations: — 

Horolog.  lunbnlftt.  'oinp.  corr. 

2.  49.  50.  Altitudo  Lyrao 71.0  8.' .     2.50.31. 

2.  52.    o,        "  "  70.  S°'        ...;./..     2.  S3.  44, 

14 75  Ap,  2 


io6 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


2.  53.  32.  Altitudo  Lyrao     ....    club.  70.0  32.' 2.  56.  51. 

3.  38,  15.  T?  Tegiincipiebat                                              3-38.15. 

3.38.39.  ^  oraniiio  tectiis;  alt,  J  limb.  inf.  i6.°  57.'       3- 38.  39. 

3.  46.   .0.  Alt.  0 circa    i.o  o.'  o." 3.  46.    o. 

S-2i-2t     "    "       12.40 5.22.    s- 

S-  26.  58    "    «<       13.  17 s.  26.  38. 

S-3t-29    "    "        13-42 5- 29- 42. 

Vage  61^.— OccttllaUo  riejadum.    1672.  Novem.  6.  inauc.      "        • 

II.     M.        8. 

HoroloR.  amb.  12.  51.    o.  riejatluin  praeccdens  omnium  a  Num.  tecta  iY  J. 

I.    2.  45.  In  cuapido  occid.  b  Num.  i  it  5  tecta  ad  Stagnnm  Miris 
V  .     supra  Paludem  Maraeotidem. 

I.  21.  31.  Plejadnm  Lucidam  proximo  praeccdens  d  tecta  ad  Montem. 

h.  m.     8. 

Acabe  &  Paludem  Arablae i.  24.    o. 

2.22.    o.  Altitudo  Procyonls,  34.0  S9-'       2.24.15. 

2-   24.  26.  "  "  35.     14 2.  27.      3. 

The  altitudes  of  Procyon  give: — : 


Mean  Times. 

Uiff.  from 
Hevklius. 

Clock-cor- 
rection. 

/;     m    .  s 
14      7    27 
14     10      5 

m       s 

-  16    48 

-  16     53 

m      s 

-  14    33 

—  14    21 

Tlie  differences  from  IlEVELirs  exceed  the  equation  of  time  by  48'  and  58'  re- 
spectively. The  clock-correction  at  14''  23'"  is—  14'"  27"^  17".  The  interval  of  one 
hour  and  more  between  this  time  and  that  of  the  occultations  considerably  increases 
the  uncertainty.     The  resulting  Greenwich  times  are : — 

Immersion  of  Coeleno 1 1"*  21""  57'±3o' 

Immersion  of  Taygeta 1 1'' 33"  42'±28' 

Immersion  of  Maia 11'' 52'"  28'±25'. 

Page  628. — OccuUatio  Pln%dum.    1673.    Martii,  22.    Die  5  ,  vesp. 

Horolog.  amb.    7.  21.  30.  Altitudo  Psililicii .    .    .   35.°  50.'    Temp.  corr.    7.24.57. 
7- SS-    o.  Praeccdens  Num.  I.  6.    In  cuspide  Occidentali 

■  PlejadumtlLuna.  . .  tegebatur 7.  58.    o. 

7.58.    o.  Plejadum  una,  sed  Globo  baud  adscripta,  tecta 

tuit 8.    I.    o. 

8.    7.    o.  Altitudo  Palilicii      .     .    29.    39 8.  10.    8. 

8.    9.    o.  Alia  PI,  N.  4.  ex  illis  arctioribus  duabus  prae- 
ccdens ...  rursus  tecta   8.  12.    o. 

_    *;    i      V       t  ,         8.  14.    o.  Ex  bis  posterior  Num.  5.  tecta  fuit  fere  eo 

ipso  J  loco 8.  17.    o. 

,      Ai,=         8,  57.  10.  Altitudo  Procyouis  .    .    36.055.' 9.  o.  52. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


107 


Comparison  of  Hevelius's  times  with  the  mean  times  computed  from  the  ahi- 
tudeB : — 


Mean  Ti 

Diff.  from 

Clock-cor- 

Hevelius. 

rection. 

h     tn 

s 

m      s 

m       s 

7     32 

25 

+  7     28 

+  10     55 

8     17 

35 

+  7     27 

+  10     35 

0      7 

58 

+  7       6 

+   10    .48 

The  moan  dock-correction  is+  10"'  46",  and  there  is  no  evidence  of  any  sensibh 
rate.     Adopting  this  correction,  tlie  resuUs  are  : — 


Greenwich  mean  time  of  imnifrsion  of  Taygeta 

Greenwich  mean  time  of  immersion  of  m  PI.   .     .  . 

Greenwich  mean  time  of  immersion  of  Asterope  .  . 

Greenwich  mean  time  of  immersion  of  I  PL     .     .  . 

I'iige  658. — Occultatio  I'leiadum  1674  Aiigusti  24.  luiiiu!  Die  9. 


6''  54™  ID" ±25" 
7"  5'"  lo'ias' 
7''  10'"  IO»±25' 


Ilorolog.  ainb.  12. 

57- 

30- 

12. 

59- 

3°- 

I. 

37- 

0. 

2. 

4- 

3°- 

2. 

21. 

3°- 

2. 

28. 

0. 

SIC. 


iO-  3°- 


2. 

47- 

0. 

2. 

57- 

0. 

3- 

0. 

0. 

3- 

6. 

40. 

3- 

12. 

20. 

3- 

45- 

IS- 

4- 

3- 

55- 

Altitiulo  Aquilao  26.  51.  dub.    .    tcini).  cor. 

"  "        26.31 

St,  inf.  praecedens  occultatii 

Praecedens  omniuui  N.   i    Lunaiii  subiii- 

gressa 

Iiileriorum  seq.  N.  5.  Luiiam  subiit   .    .    . 
Praecedens  oinninni  rnrsus  in  conspectam 

prodiit 

liucidam  praecedens  N.  4.  circa  linibura 

superiorem  !)  (ubi  praectul.  om.)  tectaest 
Inferiorem  praecedens  sese  rursiis  sistebat. 

Lucida  PI.  sese  subduxit 

Lucidani  praecedens  exiit    ..... 
Altitudo  Markab.  Pegasi.  39.°  23.'   .    .    . 

Inferiorem  sequens  eniersit 

Altitudo  Capitis  Audroniedae  54.°  12.' 
Lncida  Plejaduni  N.  6.  rursus  illuxit     .    . 


59-   54- 

2.  27. 

40.     o. 


7-  30- 
24.  30. 


31- 


2 

39- 

3°- 

2 

S°- 

0. 

3- 

0. 

0 

3- 

3- 

0 

3- 

9- 

3f 

3- 

IS- 

20 

3- 

48. 

16 

4. 

6. 

S5 

The  results  of  the. altitudes  are:- 


Mean  Times. 

Diff.  from 
Heveuus. 

Clock-cor- 
rection. 

A     m 

s 

Ill      s 

Ill        s 

13       I 

38 

+   I     44 

+   4       8 

13       4 

10 

+  I     43 

+   4     40 

15     II 

10 

+  I     32 

+  4     3'' 

■5     49 

52 

■h  I     36 

+  4     37 

The  mean  clock-correction  is  -|-  4"  29',  wliich  I  shall  consider  constant.     The 
mean  times  thus  resulting  are  given  in  a  subsequent  section. 


io8 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


The  equation  of  tiino  is  +  '"'  57")  «<>  t'l'it  the  moan  systematic  ditterence  from 
IIev£lius  is  about  20'. 

Pugo  684. — Oocultatlou  duriiip  lunar  eviijisc,  iG-j^,  ?  ,  .I.iiiiMi'y  ii,ev. 

The  clock-times  are  not  given,  but  only  those  corrected. 

II.      M.      H. 

8.    o.  50.     Stellula />  tectti  alt.  I\I.  Koiiiii;  simI  cxiro  illaii)  noil  ilepivliendi. 
8.  35.  20.    Stc'UiiIa  snprema  i\  Tergo  rolliicis  v  oiiiiiiiio  tecta, 

8.  51.  25.    Stellula  (7  ad  ipsiuii  Liuibiuii  iiiferiorein  tecta. 

9.  9.  10.     Haec  eadeiu  Stella  0  riirsns  eiiuM si f. 

The  altitudes  from  which  the  clock  was  corrected,  taken  before  and  after  the 
eclipse,  are  given  as  follows: — 

Tuiiipiis  sec.  liurol.  ; 

ex  nltit.  corr. 

h     111     s  o       ,      // 

6  22  18    AltltudoCiiiulae  Cygiii 
6  25    4    AltitudoOaiulae  (J.vgiii 

10  58  35     Altitude  Lucidac  T 

11  II  2i    Altitudo  Oapellac    .    . 
II   15  20 
II  16  59 
I.  18  37 


u 


3') 

3 

0 

38 

41 

0 

28 

5^ 

0 

70 

1 1 

0 

69 

39 

0 

69 

24 

0 

60 

I  ( 

0 

The  mean  times  computed  from  certain  of  these  altitudes  compare  iis  follows  with 
the  apparent  times  given  by  IIevelius  : — 


Mkvelu's's 
App.  Time. 

A    m      s 

Compnted 
Mean  Time. 

A    in      s 

Eq.  T 

inc. 

A  PI 

.  Time. 

App.  Error 
of  Ukvki.ius. 

m     1 

Corr.to  He- 

VKi.iiis  on 

Mean  Time. 

///     s 

m 

J 

A 

m 

s 

6     22     iS 

6     30     20 

+  s 

55 

6 

21 

25 

+  0    53 

+  82 

f>     25       4 

b    33       5 

+    8 

55 

6 

24 

10 

+  0    54 

+   8       I 

10     58     35 

II       5     55 

+   S 

59 

10 

i(> 

if> 

+    I     39 

+    7     20 

II     II     33 

II     18     57 

+  9 

0 

II 

9 

57 

+    I     56 

+   7     24 

II     iS     37 

II     26       0 

+  9 

0 

II 

n 

0 

+   I     37 

4-  7     23 

The  deviation  of  more  than  a  minute  from  Hevelujs  is  embarrassing;  but  I  can 
get  no  other  result  from  his  altitudes  than  that  given.  I  shall* therefore  take  -f  7"  42' 
as  the  corrections  to  reduce  the  times  given  by  IIevelius  to  mean  time,  from  which 
we  shall  have: — 


Locul  nionn  time.    Oncnwich  mean  time. 

8'-     8'"  32'         6''  53"'  56" 


Immersion  of  *  ?> 

Immersion  of  *  c  (85  Geminor.)       .     . 

Immersion  of  *  (^ 

-  Emersion    of  *  0(85  Geminor.)      .     . 

Page  fi^.— Solar  eclipse  of  1675,  Juno  23,  A.  M. 

He  seems  to  have  used  no  clock  at  all,  but  to  have  got  all  his  times  from  a  sun- 
dial, giving  only  the  minutes. 


8"  43-" 

2" 

7"   28'»  26 

8"  59" 

7' 

7"  44"  31 

9''   t6"' 

52" 

8"     2'"   16 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  109 

Piijjo  768. — /v'o//j>.vt.v  iVt)/is.  1676.  Die  Jovis  II  Jiiiiii  «h/c  Hi<fr«V. 

Iloro  it  is  ii  little  iloiibtfiil  how  IIkvelius  got  his  times.  His  first  coluum  is  on 
the  first  page  headed  "Jiixta  Sciater.  ct  Ilorolog.  Oscil.",  and  on  the  second  i)ago 
"Tonipus  juxta  Sciatericinn".     Jhit  all  the  times  are  given  aecnrately  to  seconds. 


Jiixia  Sciatcr. 

&  Horolog. 

Oscil. 

Allitudo 
Solis. 

Tcinpiis  e.\ 
all.corrcctum 

Magnit. 

I'hasiiiiii 

Digit. 

/ 

7.   58.   10. 

36.     17.' 

7.   53.    18. 

to. 

22. 

42. 

to. 

22. 

22. 

4l.el  pauU)  plus. 

8.     I.  30. 

36.     41. 

8.     I.     6. 

to. 

26. 

19. 

to. 

26. 

0. 

4.i.  fere. 

8.     3.   30. 

37-       3. 

8.     3.   39. 

10. 

35. 

24. 

to. 

35- 

6. 

4. dig.  22'. 

1).   22.   30. 

9.   22.     0. 

Initiuiii. 

to. 

"8. 

53- 

to. 

38. 

33. 

4l.fert;. 

<).   24.    10. 

. 

g.  23.  40. 

i.fciT. 

10. 

47- 

34. 

10. 

47- 

20. 

4.fuic. 

9.   24.   55. 

9.  24.  25. 

I 
■J- 

to. 

53- 

4g- 

to. 

53. 

30. 

35.fcre\      , 

g.  27.  28. 

9.  27.     0. 

h 

10. 

58. 

17- 

to. 

58. 

8. 

3i. 

g.  2g.  40. 

9.   29.   10. 

I. 

II . 

5- 

27- 

II. 

5- 

20. 

2}. 

• 

g-  33-  25- 

9-   33-     0. 

■  i. 

II. 

8. 

50. 

II. 

S. 

44. 

2I. 

g.   3^-  35- 

g.  3^.    5- 

i5.fcr  . 

II. 

22 

'3- 

II . 

22. 

8. 

13.  fere. 

9.  3g-  35. 

9-   39-   'o. 

2 , 

II. 

29. 

14. 

II. 

29. 

10. 

>  ,'„. 

g.  45.  4>h 

9...45.   25- 

2.i. 

II. 

35- 

35.        • 

II. 

35. 

20. 

.1 

9.    54.    22. 

g.  54-     0 

3!. 

II. 

36. 

59- 

II. 

3f'- 

55- 

l.paulo  plus. 

10.    3.  44. 

10.     3.   22. 

■ll. 

tl. 

37- 

55- 

II. 

37. 

53- 

Nondum  Sol  om. 

10.     8.  30. 

• 

10.     8.   20. 

45. 

II. 

33. 

35- 

II. 

33. 

35. 

Nondum. 

10.    18.   17. 

to.    18.     0. 

4.!.fei6. 

II. 

29. 

15- 

II. 

39- 

15. 

Nondum. 

If. 

39- 

40. 

II. 

39' 

40. 

Finis  Eclipscos, 

. 

. 

. 

18. 

10. 

33-     "• 

18. 

19. 

.       .       . 

•        •       • 

• 

4. 

20. 

0. 

32.     57. 

20. 

36. 

Obseri'cd  Scmidiamcters  of  the  Moon. 


H.        .M. 

, 

„ 

10.        0. 

13- 

53- 

to.     24. 

14- 

0. 

II.          0. 

14- 

50. 

Ultimo. 

15- 

0. 

Ilor.  auib. 


I.  25. 
3C.  39- 


45- 
47- 

55- 


25- 

54- 

o. 


19.  50. 
43-  45- 


o.  24, 

1-  3S-  4J. 

1.  44.  7. 

2.  46.  29. 

2-  S3-  35- 

3.  18.  19. 
3.  42.  20. 


Piige  774. — Occultatio  Martin  et  quarundam  Fixantm  1676  Sept.  1.  mand. 

II.      M.    s. 

Alt.  Ciuidiie  Cygiii 57.°  40.'  Temp.  cor.  i 

Mars  i\  Luna  oinuiiio  tcctua 

Alt.  Caiidae  Cjgni S'-  J7- 

Mars  cniicnit;  Finis  lunniio  occultationis     .    . 
Alia  Stelliila  Fi.xa  b  sub  Marte  cgrcditur     .    . 
Altitude  Sehcat  Pegasi.      ...    45.     3. 
Fixa  c  ad  Cuspidcm  Lunae  iuferiorem  observata  est, 

;  [Corresponds  exactly  with  a  MS.  at  the  Paris  Observatory.] 

Animadvertenda. 

De  caetero  notandum  est,  paallo  post  Martis  egressuiu  aliain  insuper  Stellulam  Fixam  b, 
Olobo  nlitts  nondum  adscriptain,  vix  ad  3  Min.  prima  iufra  Martcm  versiis  iVustrnm,  Honl  uimiruni 


no 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


2  S3'  35"  exiliisse circa  Paludes  Ainaras;  qiiaiu  quidoni  Lunain  siibiro  baud  aiiiinadverti;  ctiin  totus 
iu  eo  fueriin,  ut  Martis  momeutum  occultatioiiis  praecisc  deterniinareni :  •    * 

Tlie  results  of  tlie  altitudes  are: — 


Mean  Times. 

Ditr.  from 
Hevklius. 

Clock-cor- 
rection. 

/; 

m 

s 

m     s 

HI        S 

12 

59 

26 

-     0    58 

-     I     59 

13 

43 

26 

—     0    41 

-     I     59 

"5 

17 

30 

-    0    49 

—      2      20 

The  mean  correction  is  —  2'"  6",  which  may  be  considered  constant.     The  Green- 
wich mean  times  will  then  be  :  — 

Immersion  of  Mars 12''  19™  57"  ^  15' 

Emersion  of  Mars 13''  31'°  12' ±  15' 

Immersion  of  h 13''  38"  i8'±  15' 

Immersion  (?)  of  f 14''  27'"     3' ±25". 

I  have  not  succeeded  in  identifying  the  two  stars.     They  are  probably  too  small 
to  be  in  the  accurate  catalogues. 

Pago  ?>i^.—  Occxdtatio  duarnm  Stelhilantm  in  Clara  Orionis  1678.  JIart.  28  5  veap. 


II.   M.  s. 

Hor.  aiiib.  7.  31.  o. 

9.  16.  o. 

9.  17.  o. 

9.  19.  o. 


Luna  togit  iniiecedentciii  in  Clava  Orionis. 
Luuategitaliani  Stclhilam  bacteuua  iucogn.* 
Alt,  Procyoiiia  33.  18.  o. 

"  "  33.     4-  o. 

Nam  ilia  praecedens  in  Clava  Orionis  hoc  tempore  anno  sc.  cuiTeiito  1678  dcgit  secundum 
nostrum  Catalogum  in  24P  21'  10"  □  &  Lat.  30  1 1'  24"  Anst;  sic  nt  oninino  ilia  ipsa  fuerit,  quae  priua 
fuit  obtecta.    At  do  altera  posteriori  dubito,  an  ca  ipsa  fiici  it,  ilia  scilicet  in  clava  Orionis  sequeus; 

Latitudo  quidera  ejus,  quae  est  3°  21'  19"  Aust.  occultatin 1  iion  piobibct  omnino,  sed  nibilomi- 

nils  adeoarctamSj'uodum  cum  priori  Stellulanon  concodit.    *    *    •    •     250  17  n  &  Lat.  3°  13' A. 

The  clock-corrections  resulting  from  the  altitudes  are,  respectively,  +  6™  43"  and 
+  7"  I';  mean,  -f  e™  52".  The  Greenwich  mean  times  of  the  occiiltations  will 
then  be :  — 

First  star,  B.  A.  C.  1867  (f) 6^  23"'  i6»±45" 

Second  star,  ;t*  Orionis  (?) 8'"     8™  16' ±22". 

The  two  stars  are  those  of  the  British  Association  Catalogue  nearest  the  moon's 
limb;  but  it  is  doubtful  whether  they  are  really  the  occulted  stars. 

"In  the  original  MS.  at  Paris  the  minutes  were  first  14,  and  were  changed  to  16. 


RESEARCHES  ON  THE  MOTION  OF^THE  MOON. 

From  the  Annus  Clhnactericus  of  IIevelius,  Gedmii,  MDCLXXV. 
Page  7. — Occ  •  'atio  Lanck  Amtrinae  &c.  1^)79.  Mart.  30.  Mane. 


Ill 


Horol,  amb. 

Distantiac 
et  Alliludlncs. 

Quo  instru- 
mcnto. 

Temp,  corrcc. 

gr.   m.     s. 

I.  48.   30. 

Altitudo  Roguli   .     .     dub 

23.  27.     0. 

Quadr.  p.  or. 

2.  41.     0. 

Minor  Stella  occulcabalur 

2. 

45-     0. 

2.  48.  40. 

Major  Slell.T  •egcli-'.tur    . 

2. 

52.   40. 

2.   55-     0. 

Alt.  Arcturi     .... 

52.'      II.' 

2. 

50.   15- 

2.   58.     0. 

"         "           .... 

5t.         57. 

3. 

I.     0. 

3.   16.     0. 

It        ti 

50.           3- 

3. 

21.   iC. 

3.   56.  40. 

Emcrsio  Minorls  Stcllulae 

4- 

0.  40. 

4.     5-   15. 

Emcrsio  Majoris  Stcllulae 

. 

4. 

9-   >5. 

4.   34.     0. 

Alt.  Arcturi     .... 

40.         46. 

4' 

38.  29. 

4.  36.     0. 

"        "          •     •     •     • 

40.         24. 

• 

4. 

41.   14. 

Stel.  diff.  in  long.  4.'  30."  Lat.  3.'  ft 

ri.    Minor  majorcm  sequatur  in  mjijori. 

Lai.  Bor.  Long.  ejus.  1660.  10. °  16. 

0."  HI.  et  Lat.  0.  29.  30.  B. 

1 

The  results  of  tlie  observed  altitude.s  are:  — 


Rejecting  the  doubtful  altitude,  the  clock-correction  at  1 5*"  49"  was  -f  9"  30"  ±  1 2*, 
which  we  shall  suppose  constant.  Tliere  may  bo  some  suspicion  of  a  gaining  rate  to 
the  clock,  but  its  effect  on  the  mean  of  the  observations  would  be  small.  The  results 
will  be : — 


Greenwich  mean  time  of  immersion  of  a}  Libras 
Greenwich  mean  time  of  immersion  of  a^  Libne 
Greenwich  mean  time  of  emersion  of  a'  Librse 
Greenwich  mean  time  of  emersion  of  oc^  Libra; 


1 3' 3 5'"  54"  ±2  2' 
i3'43"'34'±20» 

14"  51"  34' ±15' 
i5'»    o'"    9"  ±16" 


I  I  2  RE.SEARCIIES  ON  THE  MOTION  OF  THE  MOON. 

Piigo  i8. — OccuUatio  U,  1679.  Juiiii  5.  man6.      (  rose  at  15''  35"'.) 


Hor.  Ami). 

Dislanliac  &i 
allitudincs. 

Tcropus  correct. 

I.    18.    55. 
I.    29.     0. 
4.    15.    40. 

4.  if..      9. 
4-     16.    35. 

5.  14.      0. 
5.    14.    20. 
5.     14.    45- 

ID.     22.     30. 
10.    27.    16. 
10.    30.      8. 
10.    38,      0. 
10.    45.    28. 

All.  Capitis  Andromedac 

All.  Arcluri 

Jupiler  slringcbat  J  linibum 

"       ad  ceiilrurn  usque  occullabalur 

Jupiler  lotus  omnino  tectus 

Jupiler  denusexircvol.ibili  parliculA  videbatur 

Oimidius  Jupiler  exiveral 

Tolus  Jupiler  omnino  prodiit 

Alliludino  Solis 

II             II 

24.    52.      • 
3'.      3.      . 

53.    34.    40. 

53.  59.    45. 

54.  14.      0. 
54-    53.    40. 

55.  27.    20. 

II.      M.         S. 
I.     20.     54. 

I.     31.     24. 

4.    is.     5. 

4.     >8.    31. 

4.  19.      0. 

5.  I&.    25. 
5.    16.    45. 
5.    17.     10. 

10.    25.      2. 
29.    42. 
32.    26. 
40.    26. 
47.    4f>. 

Results  of  the  observed  .altitudes: 


Object. 


n  Andromeda: 
Arcturus 
Sun    .     . 


Mt-an  T 

inc. 

// 

m 

s 

>3 

18 

50 

>3 

29 

4 

10 

22 

44 

10 

27 

9 

10 

30 

12 

10 

37 

54 

10 

45 

13 

Diir.  from 
Hkvki.ius. 


4 
20 
18 
33 
14 
32 
33 


Clocli-cor- 
rcction. 


m 

—  o 

+  o 

+  o 

—  o 
+  o 

—  o 

—  o 


5 
4 
14 
7 
4 
6 

15 


The  niefiii  dock-correction  is  — 2",  without  any  sensible  rate, 
mean  times  of  the  observed  jihases  are:  — 


Immersion. 

Contact  of  limbs  . 
Jupiter  half  covered 
Jupiter  entirely  hidden    1 5''  i 


15"  I' 
15"  I 


2"dh7"- 

3 1"  ±7". 

57"  ±7"- 


KnierBion, 

Partly  emerfyed     .     . 
Half  emerged 
Entirely  emerged 


The  Greenwich 


15"  59™  2  2"  ±7". 
15"  59  42"  ±7"- 
J  6''    o'"     7"  ±7". 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Page  27. — 1679,  Jiiiiii  24.  vesp,  Oocultatio  duarum  atellidaruM  in  t . 


113 


Hor.  ami). 


h.  m.  s. 

10.  30-  55. 

10.  41,  51, 

11.  o.  8. 

11.  40.  55- 

12.  II.  48. 
12.  13.  8. 

12.  17,  25. 

13.  ig.  ig. 
12.  22.  52. 


Allitudo  Arcluri 

Inilium  occull.itionis  j|<  majoris 

Exitus  ejus  Stellae  in  /     . 

Alt.  Arcturi 

II  II 

Alt.  Lucidae  Coronae  ... 


Distantiae  & 
altitudincs. 


Quo  instruniL'nto.  Tcmpus  correct. 


42. 
42. 


48. 
31  • 


30.  58. 

2().  .15. 

46.  9. 

45-  53- 

45-  23. 


Quad.  p.  or. 


10.  44.  22, 
io.    46.  32. 

11.  4.  28. 

11.  45.  15. 
i'.^.    16.  20. 

12.  17.  49. 
12.    21.  42. 

23.  36. 

27  10. 


Major  ilia  Stella  est  media  illi  in  praeccdente  fascia,  t . 


Results  of  the  observed  altitudes  : 


Star. 

Mean  Ti 

mes. 

Diff.  from 
Heveuus. 

Clock-cor- 
reclion. 

A 

m 

s 

m     s 

m     s 

Arcturus 

10 

45 

57 

+   I     35 

+  6       2 

" 

10 

48 

5 

+   I     33 

+  6     14 

" 

12 

17 

55 

+    I     35 

+  6       7 

" 

12 

19 

26 

+   I     37 

+  6     18 

11  Corona) 

12 

22 

25 

+  0    43 

+    5       0 

" 

12 

24 

•9 

+  0     43 

+   5       0 

" 

12 

27 

54 

+  0    44 

+  5       2 

The  difference  of  more  than  a  minute  between  the  ck)ok-corrGctions  given  by  the 
two  stars  is  quite  embarrassinfi;',  and  the  more  so  that  IIeveliu.s's  cah-uhition  makes 
them  nearly  agree.  The  equation  of  time  was  i  45',  so  that  the  error,  whatever  it  is, 
seems  to  be  in  the  computations  relating  to  a  Coronic.  The  positions  which  I  have 
adopted  for  the  stars  are ;  — 

!  Arcturus,    R.  A.  =  14''     i""  4";  Decl.  =  + 20°  52'.5  ; 

aCoronaj,  R.  A.  =  15''  21™  7";  DecL  =  +  27°  49'.5. 

In  the  observations  of  1663,  August  18,  the  same  two  stars  were  observed,  and 
there  Heveluis's  computations  agree  with  mine.  At  present,  the  only  course  seems  to 
be  to  reject  the  altitudes  of  a  Corona?  entirely,  and  adopt  the  clock-correction  +6'"  10" 
resulting  from  the  altitudes  of  Arcturus,  which,  it  will  be  seen,  is  only  about  10''  greater 
than  that  resulting  from  Heveluis's  computations  of  a  CoroniB,  when  corrected  for 
the  equation  of  time.     The  results  are  then :  — 


Greenwich  mean  time  of  immersion  of  p  Sagittarii 

Greenwich  mean  time  of  emersion 

15 75  Ap.  2 


9"  51     42'±6» 
iqI.  2 a"-  29'  ±6». 


114  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Page  no. — Occultatio  Palilicii.  i6Si.  Jan.  I. 


Hot.  amb. 

?•     37.       0. 

Stella  occull.nta  csl.  alt.  capitc  Androm. 

50. 

3a. 

7. 

37- 

33. 

7.     46.       0- 

Altitudo  Capitis  Andromcdae    .     .     , 

49. 

24. 

7- 

46. 

II. 

7.     4q.     30- 

48. 

55- 

7. 

49. 

8. 

8.     46.       0. 

Paliliciiim  rursiis  afl'ulsit      .... 

8. 

44- 

0. 

8.     SI.       0. 

Alt.  Cap.  Androm.  extitit     .... 

40. 

22, 

8. 

49- 

8. 

Results  of  tlie  altitudes :- 


Mean  Times. 

Dlff.  from 

Clock-cor- 

Uevemus. 

rection. 

Ami 

m     s 

m     3 

7    4!»    37 

+  5      4 

+  5     37 

7    51     14 

+  5       3 

+   5     14 

7     54    53 

+    5     45 

+   5     23 

8    55     55 

+  6    47 

+  4    55 

Here  again  there  seems  to  have  been  an  error  in  Hevelius's  computations  of 
apparent  time.  But  there  is  little  doubt  of  the  mean  dock-correction  -4-5™  17' ±8"; 
applying  which,  we  have : — 

Greenwich  mean  time  of  immersion e*"  27"  41' ±  20' 

Greenwich  mean  time  of  emersion 7'' 36"°  4'' i ''7'' 

Page  139. — OocuUatio  Palilicii.  1683.  Jaa.  c).  vesp,  ,.  ; 


H 

or.  amb. 

8. 

54.     30. 

Alt.  Pollucis       .... 

.     .       48. 

43. 

Quad.  p.  or. 

9- 

0. 

5. 

8. 

55-     15- 

"        "           .... 

.     .       48. 

53. 

9- 

I. 

22. 

9- 

42.     15- 

Initium  occultationis    . 

9- 

48. 

15- 

9- 

30.     40. 

Alt.  Reguli 

.     .        24. 

12. 

9- 

56. 

35- 

9- 

54.     15- 

"         

.     .        24. 

40. 

9- 

59. 

5«. 

10. 

55-     30. 

Finis  occultationis  Pal. 

.      . 

• 

II. 

I. 

30. 

3.     58. 

Dist.  Pal.  ab  occ.  ([   limb.    7 

rev.    . 

5-     '9. 

9- 

58. 

9.     10. 

"              "               "          10 

. 

7.     36. 

«5. 

10. 

13.     20. 

"          12 

9.       7. 

19. 

20. 

19.       12. 

Alt.  Reguli 

.      .        36. 

16. 

II. 

25. 

32. 

21.         2. 



.      .        36. 

22. 

. 

II. 

26. 

20. 

23.      20. 

"        "         

.      .        36. 

40. 

• 

II. 

28. 

46. 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

From  tlio  iiltitiulos  wo  havo  :  — 


115 


Star. 

Mean  Ti 

IPCS. 

Dlff.  from 
IIkvemus. 

Clock.cor- 
rcclion. 

h 

/« 

/ 

m     s 

m     [t 

Pollux 

9 

8 

«4 

+   8       9 

+  "3    44 

" 

9 

•  8 

49 

+   7     37 

+   «3    34 

Rugulus 

10 

4 

49 

+  8     l» 

+  »I4      9 

" 

10 

8 

4 

+  8     .3 

+   13    49 

' 

II 

33 

47 

+   8     15 

+    >4     35 

41 

II 

34 

36 

+  8     16 

+   13    3t 

" 

II 

37 

3 

+  8     47 

+  «3    43 

Tlie  niojin  clock-corroction  is  +13'"  53'±6",  vviiich  sooins  to  Imvo  been  constaiit. 
Wo  then  havo:  — 

Greenwich  moan  time  of  Immorsiou 8'' 41'"  3  2"  ±8' 

Greenwich  mean  time  of  emersion       Q*"  54™  47' ±  8". 

Pago  145. — Occult,  duarum  *  sub  cornu  aunt.  8  .  168,3.  iipr.  2.  vesp. 


Hor.  arab. 

Tempus  cor- 
rect. 

9.   54.   30. 

9-   53.     0. 

Initiuni  occul.  Sicllac 

Maj.  A.  5.  mag.  . 

10.  29.  36. 

"           "          Stcllac 

H.  6.  mag. 

10.  30.  36. 

10.   52.   50. 

Finis  occult.  St.  A. 

10.   53.   50. 

II.  43-   30. 

Alt.  Lyrae    . 

3i-° 

25-' 

II.  44.   16. 

II.  45-   30. 

II                 K 

3'. 

44. 

.      .      .      . 

.     46.   47- 

n.  46.   30. 

II                 II 

31- 

55. 

.      .      .      . 

.     47-   42- 

II.  47.  30- 

' 

32. 

6. 

.     49-   27- 

Tlie  altitudes  of  a  Lyrai  give :- 


Mean  Times. 

Diir.  from 

Clock -cor- 

Hevemus. 

rection. 

h     m 

s 

m     s 

m     s 

II     48 

17 

■+■  4       I 

4-  4     47 

II     50 

40 

+  3     53 

-t-   5     '<> 

II     52 

I 

+  4     19 

••  5     31 

II     53 

22 

+  3     55 

-»-  5     52 

The  mean  correction  is  +5"'  20'  ±14',  which  corresponds  to  the  clock-time 
1 1*"  46"'.  We  have  no  data  for  clock-rate ;  but  for  several  years  it  has  appeared  too 
small  to  be  indicated  by  such  observations  as  Hkvelius  could  make.  Applying  this 
correction  to  the  occultations,  the  Greenwich  mean  times  are: — 

Immersion  of  119  Tauri 8"  43""  44' ±  24' 

Immersion  of  1 20  Tauri g"*  20"  20»  ±20' 

Emersion    of  119  Tauri 9"  43"  34' ±1 8'. 


ii6 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON, 


§   ID. 


tS 


()I!Si;i;VATIONS  OF  KCLII'HKS  AND  OCCIJLTATIONW  MADK  IIV  ASl'IfONOMKUH  OF 
TUK  FltKN(;il  HCIlOOIi  ItKTWKKN  1670  AND  1750,  AH  FOI'NI)  IN  TlIK  MANU 
SCmi'T  IMiCOllDH  OF  TIIK  PAIMS  AND  TIIK   ^^^.KOV^^^   OKSKKVATOHIKH. 

Wc  now  i)iiss  to  a  cliiss  i)i'  uliscrvutiuiiH  imicli  iimro  siitisfnctory  tliiiii  tliono  witli 
wliicli  \v«'  have  ht'Oii  tU'alinj;'.  In  llio  latter  part  of  tlic  scxciitcciitli  I'ciitiiry,  I'icakd 
and  otlior  Kroncli  astrononicns  introduced  the  improved  nietliod  of  dctcrnMuin;;'  tliu  time 
by  eqnal  altitudes  of  the  Mun,  of  wliicli  I  have  already  spoken.*  Their  clocks  were  H(» 
far  improved  that  tlusir  j)rincipal  chanj^es  of  rate  were  tliose  due  to  ciian;^es  of  temper- 
ature. I  include  in  tla^  present  section  all  the  (di.servatioiis  for  whicii  the  time  was 
determined  on  this  plmi,  includin;^'  those  of  Dei.isi.k  in  St.  i'etersl)urj;'.  They  are 
for  the  most  part  nn|mlilished.  The  results  of  a  few  have  indeed  appeared  in  the  (dd 
Memoirs  of  the  French  Aca<lemy,  and  in  the  P/dlosnpliiad  Tninsartions,  hut  these  are 
not  by  any  means  the  most  valuable  ones  f(U'  our  ))r('sent  jiurpose.  IJositles,  Miey 
were  reduced  with  the  imperfect  data  of  the  time,  and  need  a  more  carefid  reduction 
before  the  best  results  can  bo  obtained  from  them.  As  an  example  of  the  daiiffer  of 
trustinnf  to  the  old  reductions,  it  may  be  remarked  that  occultations  were  often  observed 
by  Cassini  with  a  ditferent  clock  from  that  u.schI  for  observing'  the  meridian  observa- 
tions of  the  sun.  Hut  in  conunnnicatinf^'  the  result  of  one  of  these  observations  to  the 
Academy,  he  failed  to  correct  it  for  the  ditt'erence  of  clocks,  so  that  it  ajtpoars  printed 
in  the  Memoirs  more  than  a  minute  in  error. 

J"'our  occultations  of  the  Pleiades,  observed  by  Dei, i.**!.!:  at  St.  Petersburg-,  were 
reduced  by  li].Ns,sKH,  of  the  I'idkowa  Observatory,  aiul  ])ublished  in  the  ^lemoirs  of 
the  St.  Petersburg  Academy.f  Hut  observations  of  occultations  were  made  by  Delisle 
durinp-  a  large  part  of  his  stay  at  St.  Petersburg,  whicli  are  to  be  included  in  any  com- 
plete discussion  of  the  subject 

In  March,  1871,  the  late  M.  Delaunay,  then  director  of  the  Paris  Observatory, 
very  kindly  placed  the  whole  of  its  older  archives  at  my  disposal,  with  unrestricted 
permission  to  extract  from  them,  and  use  in  my  investigations,  whatever  I  might  find  of 
value  for  the  work  in  hand.  Two  years  later  a  similar  permission  to  comi)lete  my 
copies  in  certain  points  was  granted  by  M.  Le  Verrier.  As  a  result  of  this  permis- 
sion, I  am  enabled  to  present  the  observations  discussed  in  the  })resent  section. 

Of  the  records  to  be  used,  a  large  portion  were  evidently  never  intended  to  be 
understood  or  used  by  any  one  but  the  observers.  For  the  most  part,  the  note-books 
contained  no  titles,  no  indications  of  the  observer,  no  verbal  statement  of  the  oljserva- 
tion,  and  no  name  or  indication  of  instruments,  excei)t  in  the  case  of  clocks.  All 
information  on  these  points  liad  to  be  gained  by  comparison  and  iiuluction.  It  was 
found  that  a  certahi  arrangement  of  figures,  which  the  reader  soon  learned  to  recog- 

•  See  an/t;  pp.  23-24. 

t  lltrvon  Dc  I' Isle  beobcuhtcte  PUjaden-Bedeckungen,  bearbeitet  iind mil  Hansen's  Atondta/etn  verglkhen,  von  C.\RI. 
LiNSSER.    St.  Petersburg,  1864. 


RESF.ARCIIES  ON  THE  MOTION  OF  T1IE  MOON. 


117 


nize,  Hhowed  olworviitidnH  of  o(iiiiil  nltitiideHof  tlio  huh  hoforo  and  utter  ii(k»ii,  mid  timt 
tlu)  si^riift  {(  uiid  )|  indicated  tlio  tniiiHitH  of  tlio  two  liiiilm  of  tli(3  huh  ovit  tlio  iiutriditui 
(»t'H(»iii()  iiiHti'iimoiit.  Much  oltsctrvcr  schmms  to  liiivo  liiid  his  own  instruinents,  wliich  h(f 
nHud  withont  iiiiy  rrtcronco  to  or  coinitiirisoM  with  tlie  instruments  ot'  otliors.*  In  niiiny 
uiiHOH,  OHjH  (iiiilly  anion}r  tho  oiirliur  olisorviitions,  no  <h'si;;inition  of  the  occultod  star  by 
wliicli  it  nii;;ht  Ik*  identitiod  whs  friven.  In  these  ciisc^s,  it  was  necessary  to  coinpnte 
the  talndar  place  of  tlie  moon,  as  atVccttMl  hy  paraUax,  foi'  the  tinm  and  phice  of  the 
oc'cnItatioM,  and  then  to  asc(;i'taiu  from  flie  modern  (;atah)^iuis  or  star-maps  what  stars 
were  then  noiir  eontact  witli  tlio  limb  of  the  moon.  I  boliovu  this  oi)oration,  tli(ni;;h 
laliorions,  was  always  successful,  except  in  a  few  oasos  of  sturn  too  faint  to  be  found 
in  cataio;,'ues. 

In  tlu!  followiufr  pa<,'Os,  the  intention  is  to  present  literal  co|)ieH  of  extracts  from 
the  ori<,'imd  records  It  is  not,  h(»wovor,  uiways  practi(!able  to  do  this  with  entire 
rijj^or.  In  the  case  of  some  ol)servers.  especially  of  Dki.isi.k,  the  <d)S((rvations  were 
{jfiven  at  sindi  len^ftli,  and  mixed  with  so  many  extended  ren>'>"ks,  that  a  condensed 
summary  was  absolutely  necessary.  These  sunnnaries  can  always  be  distin<;uislied 
from  verbatim  copies  by  bein;;'  written  in  Kni^lish.  In  printin<r  the  followin<f  discus- 
sion of  tlu*  (djservations,  a  shcrp  distiiuition  is  made  between  two  clas.ses  of  matter, 
namely,  (i)  remarks  maih'  at  the  time  of  examinin;,''  the  ori;;inal  <djservations,  whi''! 
tho  writer  was  in  entire  i^^iua-ance  of  the  nature  of  the  results;  an<l  (2)  tlic!  ulterior 
reductions,  made  when  tho  orij^lnal  records  were  no  longer  accessible.  The  former, 
as  well  as  the  literal  copies  from  the  r(!Cords,  are  distinguished  by  being  printed  in 
smaller  typo,  so  that  the  reader  can  readily  distinguish  them  iVon>  the  latter.  The 
arrangement  is  made  on  the  tbilowing  plan: — The  ob.servatif  us  are  divided  into  four 
series,  each  of  which  aro  made  by  one  set  of  observers,  or  on  a  connnon  plan,  or 
with  the  same  instruments.  Perhaps  it  would  be  more  accurate  to  say  that  the  differ- 
ent series  correspond  to  ditVerent  sets  of  volumes  found  among  tho  archives  of  the 
Paris  Observatory;  certainly,  this  is  the  only  real  distinction  I  can  now  make  between 
series  I  and  series  IV.  Preceding  each  series  is  given  such  general  discussion  of  tho 
observations  as  ajjplies  to  tho  whole  of  it.  Kacli  series  is  divided  into  groups,  each 
group  comprehending  such  ol)servations  as  could  bo  conveniently  discussed  together, 
and  the  reduction  ami  discussion  of  tho  observations  of  each  group  are  given  innue- 
diately  after  tho  observations  which  belong  to  it.  In  tlio  case  of  series  IV,  however, 
all  the  earlio''  observations  are  made  and  reduced  on  a  plan  .so  nearly  nnifonn  that 
it  has  not  been  doomed  nocessaiy  to  go  into  the  separate  details  of  reduction  of  each 
observation. 

It  may  happen  that  in  some  cases  tho  relation  of  the  observations  to  each  other, 
and  the  bearing  of  the  remarks  on  them,  will  not  bo  clear.  This  is  owing  to  several 
disadvantageous  circumstances.  Some  of  the  archives  examined  were  inisarranged 
through  mistakes  of  the  cataloguer;  the  copies  were  made  during  the  reign  of  the 
Commune  and  tho  siege  o[  Paris  by  the  national  forces,  and  were  therefore  somewhat 

•  In  this  connection,  it  may  not  Vic  amiss  to  call  attention  to  the  widespread  error,  fuund  even  in  Krench  histories  of 
astronomy,  that  Cassini  1.  \v.is  director  nf  the  Paris  Observatory.  In  fatr,  iliisctalilishmcnt  «a.*  assigned  to  the  common  use  of 
the  astronomers  of  the  Academy  of  Sciences,  and  no  such  office  as  that  of  director  was  known  or  recognized.  The  celebrity  of 
Cassini  seems  to  have  given  rise  to  ;he  unfounded  impression  that  he  exercised  a  supervision  over  the  work  of  the  other  astronomers. 


ii8 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


hurried;  in  reading  proof,  no  access  to  the  originals  could  bo  Iwul.     These  circuni 
stav.ctis  are  the  only  apology  I  can  present  for  any  crudity  of  arrangement  which 
may  bo  noticed. 

• 
Examination  of  Manuscripts  at  the  Paris  Ohservatory. 

Series  1.  .  ■  -  •    .  .^   .    -    /'-  ■  ■ 

TliiTC  are  curious  du]  icate  copies  of  the  earlier ob.sorvationa  at  Paris,  (i)  We  liavo  a  volume 
entitled  Jlistoire  Celeste  de  VOhservatoire  Eoyal  de  Parin,  vol.  i,  1671-1675.  Jiiit  vol.  2,  witli  the 
eauie  title,  does  not  begin  until  1783,  and  the  similarity  of  the  volumes  following  2  to  volume  i 
seems  to  show  that  they  were  not  prepared  until  a  comparatively  late  date. 

(2)  There  is  another  volume,  entitled  Fragment  des  Releves  des  liegistresde  VOhnervatoirr  Royal 
de  Vans,  in  which  the  observations  of  1672,  1673,  1680-1684,  1700-1703,  1760-1767,  are  copied  on 
j)rinte(l  forms,  with  the  beading  Histoire  Cdleste  de  VOhservatoire  Royal  de  Paris,  which  was  prepared 
by  Cassini  IV.  for  publication,  but  never  published. 

These  two  volumes  seem  to  be  in  the  same  handwriting,  namely  that  of  Cassini  IV.  Yet, 
while  much  of  the  matter  in  the  two  is  common,  each  contains  observations  and  remarks  not  given 
in  the  other.  Fo>  instance,  in  the  case  of  the  occultations  of  February  3,  1672,  (2)  says  that  the 
clock  stopped  about  5^  hours  i).  m,,  and  that  it  stopped  very  frequently  about  this  period.  There 
is  no  complaint  of  the  clock  at  all  in  (i).  Yet  the  observations  agree  perfectly.  But  of  the  alti- 
tudes for  time  copied  from  (i)  only  a  very  few  are  found  in  (2).  More  curious  yet  is  the  comparison 
of  the  accounts  of  an  occultation  in  1672  given  in  the  two  registers,  which  I  copy  verbatim. 

From  (i),  page  32. — "  Le  2  Aoust.  Vers  Ic;  J'',  du  soir  la  lune  etoit  proche  d'une  etoile  fixe 
voisine  d'Autar<5s  qu'elle  a  eclyps(5e  au  moment  de  I'immersion  (qu'ou  a  oublii;  de  maKpier  sur  le 
registre)  la  distance  on  la  differ,  de  decliu.  du  bord  austral  de  la  lune  et  do  I'etoile  etoit  do  i'  3"." 

From  (2),  p.  42. — "Aoust  le  2.  Vers  les  9''.  du  soir,  la  lune  s'appro  J..,.t  d'une  etoile  voisine 
du  coeur  du  Scori)ion  que  I'on  a  jug6  devoit  6tre  eclypsde.  Le  parallelle  de  I'etoile  parait  quelques 
miuutes  au  raidi  de  la  tache  de  Copernic. 

"  10''.  21'.  34".    Occultation  de  I'stoile  par  la  lune  {10''.  2^'.  n",  T.  vr.)" 

We  find  also  that  in  (2)  the  use  of  the  astrdnomica'  "ly  is  introduced,  instead  of  the  old 
divisions  "  matin",  "soir",  and  we  have  the  following  clock-errors  ai'.d  transits: — 


Aug.  2. 


8"  22' 

0' 

12   17 

5 

14  44 

0 

15   13 

0 

9  56 

0 

'o  35 

0 

Pend.  retard .  o'  35" 

/9  versau  au  merid 34°  12'  55" 

Mars         "      "        32     57   30 

Saturn       "      "        39     37    4° 

Pend.  retard o'    42" 

a  Aquilae. 


[In  (x),  10''  34'  40^'  is  giveu  for  the  time  of  transit  of  a  Aquilae.] 

But  there  is  no  indication  how  these  clock-errors  were  obtained,  and  no  obsers^atious  in  either 
book  to  fix  clock  errors  at  these  times. 

I  infer  from  this,  and  also  from  remarks  of  Gassini,  that  b(vt'«  voluTties  are  simply  excerpts 
from  registers  which  cannot  now  be  found,  and  that  the  observations  of  different  i»ersons  are  mixed 
together. 

The  clock-error  would  seem  from  what  follows  to  be  well  determined,  unless  the 
InGtruments  for  determining  it  were  erroneous.     But  the  times  of  transits  winch  follow 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  1^9 

do  not  agree  with  this  error  at  all.     In  fact,  we  have  from  the  transits  of  /?  Aqiiarii 
and  a  Aquilae  : — 

1672,  Aug.  2.  Aug.  3. 

h       m       e  h       7n       a 

Right  ascension  of  star            ...  21    14  17  19  34  48 

:           Mean  time  of  transit      ....  12  24  58  10  41    50 

Apparent  times 12   19  27  10  36  24 

Clock-times 12   17  5  10  35     o 

Clock  apparently  slow 2  22                                 i   24. 

Either  the  meridian  instrument  was  defective,  and  not  used  for  clock-en'or,  or 
observations  with  two  clocks  are  mixed  together.  As  the  method  of  equal  altitudes 
was  known  and  practised  at  this  time,  I  think  we  may  take  the  clock-correction  given 
as  probably  near  the  truth,  .so  that  we  shall  have : — 

h     m       » 

Apparent  time  of  an  occultation  of  r  Scorpii,  1672,  Aug.  2  10  22   11. 

Equation  of  time 5  S'-^ 

Paris  mean  time        .     .     .     .  ' 10  27  42.6 

Greenwich  mean  time        10  18  21.6. 

In  view  of  a  certain  probability  that  the  clock-error  was  well  determined,  the 
probable  en-or  of  this  time  may  be  estimated  at  ±  6";  but  the  probability  of  the  error 
being,  four  times  as  large  as  this  is  much  greater  than  would  result  from  the  applica- 
tion of  the  usual  theory  of  errors  to  the  supposed  probable  error. 

From  (2). — 1680,  April  4.    10''  25'  7".    Occultation  d'uue  etoilo  par  la  lune. 

Midy  le  2.    11''  59'  36"  Alaligne. 

4.     II    59    SS 

6.       o      o    16.  ' 

\Yo  can  only  use  this  as  apparent  time.  The  discordant  meridian  transits  of 
the  sun  which  follow  do  not  indicate  any  readily  determined  correction  of  the  clock 
on  apparent  time.     The  equation  of  time  being  +  2'"  36",  we  have: — 

Paris  mean  time  of  occultation  of  Lalande  12 148      .     .     10''  27°  43' 
Greenwich       lo"  18'"  22". 

The  f»robable  error  may  be  ±  1 2'.  The  extraordinary  coincidence  between  the 
mean  times  of  this  and  the  last  occultation  seems  to  be  accidental. 

On  1^82,  Feb.  15,  we  find  the  occultations  of  the  Hyades  recorded  as  follows  :— 

^59    2)    Occultation  des  deux  etoilesqu'on  a  observ^esapr^s  la  lune. 

7     I  27  ) 

The  times  are  marked  in  the  column  "  Temps  vray",  which,  however,  contains  elsewhere  only 
clock-corrections.  rreceiliiiK  it  we  have  a  set  of  corresponding  altitudes  of  0  for  clock,  evidently 
independent  of  those  of  La  Hike,  hereafter  quoted,  and  {jiving  a  clock-correction  of  — 24'.3,  nearly 
half  a  minute  diilerent  from  the  correction  of  La  Uibe's  clock.  Yet  the  occultation  must  be  that 
observed  by  LA  Hire  [given  hereafter]. 


tso 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


For  this  dcM  we  have  +  14™  41' for  the  equation  of  time.  This  would  make 
the  moan  times  of  the  occultations,  as  reduced  by  the  unknown  computer : — 

h     m      s 

Oi  Tauri 7  ^3  43 

©aTam-i 7   16     8 

wliich  are  9'  less  tlian  those  which  we  shall  find  to  bo  given  by  La  Hire's  observa- 
tions.    This,  then,  may  be  regarded  as  tlie  error  of  reduction  in  the  present  case. 

Observations  hy  Cassini  and  Makaldi. 

Tliere  \»  a  series  of  registers,  in  small  quarto,  for  the  years  1683  onward,  without  original 
title  or  paging,  containing  rough  notes  of  observations.*  The  only  title  is  Observations  du  Solnil  et 
den  .EtoUen  faites  eii  Jionlogne  ct  en  Paris  Pan  1683,  H  continuee^  <i  Paris  la  meme  annie  et  la  suivante. 
No  nieution  of  the  observer,  but  there  is  little  doubt  tbat  it  was  J.  D.  Cassini. 


,    ,  EXTRACTS. 

.  1683.  Occultation  of  y  Tauri,  Feb.  5. 

Feb.  4.  Hantenrs  Eigel.    5    8  13  23    o  o 

12  47  23  30  o 

17  26  24    o  o. 

Feb.  5  (probably  a.  m.). 


9  16 


937J 
946 

H  17 
14  26 

19    I 

23  19J 
2328J 
2744 

27   S2j 

32    3 
32  12J 
36  17 
36  26J 


26 
2 


S3  h.  inf.  bord  5 

35 
b 


24    2    o 

24  30  10 

25  o    o 


o  o 


30  o 


24O  30'  o" 

24 
23 

23  o 

22  30 

22  O 

21  30 


o  o  57 
o  o  58 


midy  a  la  m.  A. 
"     a  la  m.  B. 


Feb.  5  (probably  a.  m.).  Hauteurs  lepy  delav. 


6  i8  29 
23  6J 

27  53 

32  I2j 

7  5  33J 
9  3SJ 


2330 
23  o 

i2   30 
32  O 

18  O 
17  30 


17  20 


16  29  15 


P.M. 


Ilauteurs  Uigel. 


S  «3  19 
S  18  16 

'o    432J 

9  37 


2359 
24  3« 
24  31 
23  59 


7  41  26  Rigcl  au  uierid.  par  les  h.  corres. 

12''  o'  8",  occultation  d«  I'etoile  qui  est  a  la  point  de  I'anglo  du  Hyades  par  la  luue. 
1683.  Feb.  6. 

o  I    9    raidy  a  la  m.  a, 
o  I  10      "      "     "    b. 

We    shall   derive    the  clock-carrection  from  the  meridian  transit  of  Rigel,   as 


•This  is  really  the  regular  scries  of  ihe  records  of  the  Observatory,  and  is  continued  until  1795 ;  Init  a  part  of  it  has  been 
copied  into  another  series,  which  I  have  sometimes  used  to  copy  from,  and  the  cataloguer  has  confused  the  original  with  the  copy 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  |j| 

deduced  from  the  equal  altitudes,  and  the  rate  from  transits  of  the  sun  over  the  two 
meridian-marks  on  February  5  and  6.     We  have : — 

ft      m         8 

Mean  R.  A.  of  Rigel,  1 683.1        4  59  20.1 

Sid.  time  of  mean  noon,  1683,  Feb.  5,  Paris 21      2  52.2 

Mean  time  of  transit  of  Rigel  thence  computed      ■     •     •     •     7  55     9-9 

Correction  of  clock  on  mean  time, +  1 3  44.  i 

Mean  time  of  transit  of  sun,  Feb.  5,  o''   14™  42".3;  Feb.  6,    o  14  45.8 
Correction  of  clock  (mean  of  marks)  +   13     44.8  o  13  36.3 

Correction  of  clock  for  occultation  of  y  Tauri       .     .     .     .  +  13  42.6 

Paris  mean  time 12   13  50.6 

Greenwich  mean  time 12     4  29.6. 

Ec  ipse  of  July  12,  1684. 
Le  12  Julliet,  a  6''.    Tlieriii.  79^.     Bar.  28.0. 
Haiit.  (In  bord  Nup.  du  O 
6  24  50        20  40 

27  57        21  10  ■     ■ 

31     2        21  40 
9     2  26        46  10  (f) 

5  5'        46  3° 
•  9  23  39        49  20 

Apr^-i  luidy  oil  a  avaiic6  Tkorloge  de  16".  L'Eclipse.  A  2  28  30  Elle  etoit  cominenu^e,  fin 
4  43  12.  L'borluge  de  M.  de  la  HiBiS  avaiicuit  snr  le  iiutre  5'  57".  II  a  observd  la  tin  a  sou  horloge 
a  4''  49'  9"- 

But  there  is  some  doubt  a.«  to  which  douk  the  writer  umd. 

4''  42'  56"  horloge  de  la  tour  occideiitali*  =  4  45  o  liorl.  de  la  tour  oriontiilo.     D  =  2'  4". 
1684.     Le  13  Juillet.    Ilauteiirs  du  bord  sup.  du  O 
'o    9  55  55°  30'  8"        I  49  «3i 

^■i  32  55     5°    8  I  46  32  ■ 

18  loj         56     30    o  I  40  59 

21     2  56     50    o  I  38     7  , 

23  57  57     J°  «2  I  35   '2 

26  S4j        57     30 12  I  32  '3 

33    2  58     10   o  I  26    s 

I  make  no  use  of  these  observations  of  the  eclipse.  The  beginning  a])pears  not 
to  have  been  seen.  The  coincidence  of  the  time  of  ending  with  that  derived  from  the 
observation  of  La  Hire  renders  it  doubtful  whether  the  end  was  actually  observed 
either.  The  results  of  these  and  other  observations  are  given  in  the  Mthnoires,  tome 
X,  p.  667,  where  Cassini's  time  of  beginning  is  said  to  be  2''  25"  55',  and  of  end 
4*'  43"  23'.  Either  the  same  clock-error  has  not  been  used  at  beginning  and  end,  or 
the  time  of  beginning  is  in  some  way  altered. 

1684  le  19  Decemlire.    Haut«  urs  du  bord  sup.  du  Soleil. 

9   28    10  2   35   32  10   20   o  "1  •>e&H" 

9  35  23  2  28  22  1 1     o  o 

12     o  31     1  Bord  © 
12     2  54    2      "     "  ■        . 

2  23 

12     I  34    Midy  a  la  Marque  Q 
12     2    3    Midy  a  la  .Marque  D  contre  la  Maraille. 

12    1  sii  Midy  par  les  eorresp. 

16 75  AP.  2 


122 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


A  2''  40  I'liorloge  orieiitale  avaiuie  47"  sur  I'oec.    J'ay  oste  deux  iniiiutes  a  I'horloge  oocideutale  et 
j'ay  mis  avec  elln  I'orientale. 

Le  20  Bi'cenibie. 


11  58  50  I  Bord  0 

12  I  12^  2  " 

9  S9  '8 
10  I  28 

10  3  38 

2  0  42  a 

I  58  35^ 
1  56  28 

13  10  0 

13  20  0 

2  22J 

13  3°  ° 

11  59  50    Midy  par  I'omb. 

12  o  22     a  la  Marque  D. 

[  judge  that  the  following  are  altitudes  of  the  sun  observed  on  the  monwiig  of  the  21st,  with 
a  mistake  iu  tlie  hour,  2  being  written  for  9.  There  is  a  blank  space  lett  for  the  corresponding 
Hltenioon  altitudes. 

2  32    4 

33  55 

'  35  52 

.    '  29  26 

A  midy  nebuleux  43  20 

47  13 

S«  '5 


10  50  o 

11  o  10 
II  10  30 

II  30 

11  50  10 

12  10   O 
12  30  10 


Le  21  Decembre. 


Coinmencemeut  de  I'eclipse  9'' 29'  8". 

'8  .        . 

L'Btoile  se  cache  derriere  la  hine. 

[Evidently  a  subsequent  insertion.] 

10''  8'  58"    L'Etoile  paroist.    [Under  this  another  time  is  given  for  the  same  pheDomenon,  appa 

rently  9'  10",  but  it  is  erased  with  the  pen,  and  8'  58"  is  substituted.] 


35'    6" 
-   18 


12  o  II     1  Bord  0 

12  2  34   n  " 

12  o  42     Midy  a  la  Marque  D. 


k  lo*  I'hor.  oriental  avance  sur  I'occ.  5". 


Le  22  Deceuibre. 
9 


14  46  9  10  o 

18    5  doutense.   9  30  o  dout«use. 

21  31  9  50  o 

24  57J  10  10  o 

28  30  10  30  o 


32 


10  50  o 


Le  23  Di'cembre. 
Noon  per  siugle  pair  of  altitudes,  12''  o™  30", 

Lo  24  Deceinbre. 


12  0  55  I  B.ird  du  0 

9  14  52 

2  46  54 

9  10  0 

12  3  15J  2  •'   "  " 

18  II 

2  43  34 

■J   30  0 

12  0  34  Midy  a  la  Marque  Q 

2-  37 

2  40  8 

9  50  0 

12  I  16  Midy  nou  pass,  a  la  Marque  J) 

25  '3 

2  36  32 

10  10  0 

28  36 

2  33  II 

10  30  0 

■ 

32  12 

2  29  36 

10  50 

Tliese  (tbservations  from  1684,  December  19  to  December  24,  are  {jfiveii  liere  for 
the  purpose  of  reducing  the  occultation  of  jn  Geminorum,  observed  durinj''  an  eclijjse 
of  the  moon,  on  tlie  evening  of  December  21.  The  same  occultation  was  observed 
by  La  Hirk,  with  a  much  more  certain  determination  of  clock-error;  but  I  have 


.*^' 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


"3 


thouf^lit  it  worth  while  to  reduce  these  observations  also,  aUhougli  there  has  been 
some  difficulty  in  unravelling  them,  owing  to  the  three  meridian-marks  or  instruments 
on  which  the  sun-transit  was  observed,  and  the  general  confusion  of  the  records.  The 
mode  of  proceeding  has  been  as  follows : — From  the  equal  altitudes  of  the  sun  on 
December  20  and  December  24  the  index-error  of  the  quadrant  was  derived.  Taking 
this  index-error  for  the  altitudes  observed  on  December  21  and  December  7/ 
(a.  m.  civil  time),  the  sun's  hour-angle  was  computed  for  each  of  these  observations. 
The  clock-corrections  thus  deduced  from  the  altitudes  alone,  reduced  to  noon,  were : — 


Date. 

Corr.  on 

Apparent 

Time. 

Equation  T. 

Corr.  on 
Mean  Time. 

1684. 

■f 

m 

s 

s 

Dec.  19 

+     8.0 

—   I 

40.7 

-       92-7 

20 

-     1-5 

—  I 

I0.5 

—       72.0 

31 

-   17.0 

—  0 

40.4 

-       57-4 

22 

—  24.0 

—  0 

10.3 

-       34.2 

23 

—  30.0 

+   0 

20.0 

—       10. 0 

3' 

-   50.8 

+  0 

50.1 

-         0.7 

The  correction  of  the  clock  for  the  phases  of  the  occultation  appears  tf)  be 
—  48^.2  and  — 47'.3,  with  a  j)robable  error  of  perhaps  3'.  There  is  no  certain  evi- 
dence that  the  clock  used  was  the  same  with  that  with  which  tiie  altittides  were  noted, 
but  the  close  coincidence  between  the  figures,  —  1 8,  written  under  the  observed  sec- 
onds of  immersion,  and  the  correction  of  the  clock  on  apparent  time,  make  it  probable 
that  the  clocks  were  the  same.  The  correction  —  18'  is  that  actually  applied  by 
Cassini,  as  appears  from  the  publication  of  his  result  in  the  Memoirs  of  the  Academy, 
vol.  X,  p.  674.     The  time  there  given  is  9''  34™  48'. 

The  emersion  is  to  be  received  with  suspicion  owing  to  tiie  double  record,  and 
the  possibility  that  the  observer  did  not  catch  the  star  when  it  first  emerged. 

1686,  Apr.  10.    Occultation  of  Jupiter  observed,  but  no  sufficient  data  for  clock  correction. 

Occultation  of  unknown  star,  1686,  June  25,  9^  53'  51"  p.  m.  clock. 
Juno  24,  O  altitudes. 

ID  3.     o  59  20    °  59  33    o  j^    midy.  '  '    '  ' 

33  54  59  40     o  I  54  •  '       '    • 

37     o  ^o     o    o 

June  25.    o  S3  midy.    9  S3  5'  une  flxe  dans  la  parte  obscure  J>.  '  ^        ' 

June  26.  haut.  du  bord  du  solei). 

II  58  48    -  ,0  - 


9  34  II 

52     0 

9  37  48 

52    30 

9  41     7 

52  59 

44  49 

53  30 

48  23 

54    0 

S 

cette  derniere  «e 

June  27. 

'I   58  54 
003 

1( 
1 

centre  (!). 

June  28. 

9'"  33'  43" 

5«°  5°' 

10" 

2>'   26'  26" 

37    10 

52     20 

10 

3     22   49 

June  29. 

II     59     3 

0         I      31 

l( 
)l 

■ 

124  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

The  clock-times  of  apparent  noon,  as  they  follow  from  the  meridian-  nai'k  and 
from  the  altitudes,  are  us  follows : — 


Mark. 

Altitudes  (corrected  1 

June  24 

0''     0"'  43".  5 

0"     0™  38'- 5 

25 

0"     0"  53": 

26 

11"  59"'  57". 

11"  59"  53' 

27 

0"     0"     3": 

28 

:    •       qI.     Qm      2".5 

29 


I2» 


The  clock  appears  to  have  been  put  back  a  minute  on  Jime  25,  and  there  is  no 
way  of  determining  whether  it  was  done  before  or  after  the  occultation.  The  con-ec- 
tion  on  apparent  time  at  9''.9  was  either  —  51' or +  9'.  The  equation  of  time  is 
_|_  2™  2'.     We  have  therefore: — 

Cori'ection  of  clock  on  mean  time 
Paris  mean  time  of  occultation 
Greenwich  mean  time      .... 


+   I™  II' 

or 

+    2"  11' 

9'  55"'    2» 

or 

9"  se™    2 

9"  45'"  41" 

or 

9''  46"  41 

The  star  is  B.  A.  C.  3579. 


1686.    I  Juillet.  II  ^i,  16J  |( 

:''\:     1 35  )l 

o  25 


I'oinbre  a  midy. 

L'horloge  occ.  retard  i". 

9  19  57    une  etoile  entre  dans  liiiie. 
9  37  10    elle  s'est  sortie. 
36    o    elle  estoit  sortie. 


JuiDet  2.  II  59  19    |( 

0  26    a  I'ombre. 

1  36    )l 


Following  this  are  observations  rather  difficuU  to  niiderstand,  from  which  it  is  concluded  that 
midnight  on  the  2d  was  at  o''  o™  28';  and  on  the  3d,  midy  was  o*  o""  34*4. 

Using  the  correction  of  the  meridian  from  the  observations  of  June,  we  have : — 


Transit  of©,  July  i,  clock 
Transit  of  O,  July  2,  clock 
Cassini  finds,  July  2.5  .  . 
Cassini  finds,  July  3.0     .     . 


o*"  o" 
o''  o" 
12''  o™ 
o''  o™  3 4". 5;  meantime    o*"  3 


2i".0;  meantime  t  *"  3™  9'.  7. 
22'.3;  meantime  o''  3"  2r.2. 
28";      meantime  12''  3"  26'. 7. 

3  2".  2. 


The  clock-con-ection  on  mean  time  seems  pretty  well  determined,  and  equal  to 
-f  2"  59'.  It  seems  possible  that  the  clock  used  was  the  "horloge  occidental",  one 
second  slower  than  the  other;  but  the  correction  will  still  be  less  than  3"'  o".  We 
have,  therefore : — 


Paris  mean  time  of  immersion  of  B.  A.  C.  5395  (?) 
Greenwich  mean  time  of  immersion  of  B.  A.  C.  5395  I 


9''  22" 
9"  13" 


56' 
35'. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


"5, 


I  shall  not  attempt  to  use  the  emersion. 


1689.  Miii  iS. 

53     9 

55  25 

57  23 

Mai  21. 

52  59 

53  JS 

9    6  29 

9  37     2 

Mai  22. 


Mai  24. 


)|     a  I'oct. 

K 

)|     Tiiis  time  is  i)robal)ly  2"'  early. 
lVi)y  do  la  'UJ  au  vcrticale  31  40  30. 
Iiniii.  (I'liiic  etoile  de  n  pri-H  <1«  giiiiia'uli. 
9  59  29J  '?  i)as8e  par  le  vert.  tlu.  (!) 

I( 


II  54  o J  miily. 


52  52 
55     9 

55  40  |p  liernier  l)ui'd  du  0  iiii  vert,  de  I'oetant. 

9    231  I'epi  ail  vertical. 

9  54  53  arcturiis  pa.sse  par  le  vert,  du  (jiiad. 

9  30  42  49  30  30  14  59  46 

33     I  49  50  27  53  14     )l  a"  V. 

35  21  5°  'o  25  33  2  i6 

9     o  28  I'epy  au  inerid. 

9  52  46  arcturus  au  vert. 


Notes  on  the  preceding  observations,  especially  the  list:— It  is  hard  to  say  with  certainty 
what  instruments  the  transit  of  the  sun  was  observed  with.  By  induction,  liowcver,  I  conclude 
that  the  signs  |(  and  j|  meant  transits  ol  the  suns's  limbs  over  the  meridian  of  the  octant.  Hut 
from  the  observations  of  May  21,  it  would  seem  that  this  could  not  have  bi-en  the  case  May  22. 

The  following,  however,  are  transits  of  O  centre  over  something,  and  times  of  apparent  noon 
from  corresponding  altitudes: — 


)1   1( 

Oct. 

Quad. 

Corresp.  alt 

1689.        Mai   15. 

11" 

54' 

8i" 

56" 

6» 

II   54  37 

16. 

' 

54  II 

17. 

54   13 

. 

18. 

11 

54 

17 

56 

15 

21. 

II 

'u. 

^ 
1 

22. 

II 

54 

oj 

54 

32 

23- 

1 1 

53 

56 

54 

29 

Olock  adv.  6'".  24. 

59 

56     (?) 

0     0  20 

25- 

II 

59 

S4j 

0 

23 

26. 

0     0  S4 

The  following  are  the  altitinles  of  the  sun  for  time  :— 
May  15. 


a.  ni. 

9"  54'  50" 

520  0' 

57  34 

52  20 

10     2  58 

53     0 

5  47 

i.3  20 

837 

S3  40 

54  41 
52  4 
40  30 

43  45 
4°  55 


May  23. 


ll<U^  . 

22    13 

49     0 

24  33 

49  20 

26  S3 

49  40 

29  15 

50     0 

3'  36 

50  20 

126 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


The  reduction  of  tliese  observations  has  proved  troublesome,  but  I  think  a  pretty 
certain  result  may  be  reached.  We  iiave  altitudes,  singly  or  in  pairs,  on  the  civil 
dates  May  1 5,  23,  24,  and  26.  From  a  separate  reduction  of  the  pairs  of  altitudeai 
the  index-error  of  the  altitude  instrument  seems  to  be  only  o'.i.  The  clock-times  of 
api)arent  noon  are  thus  found  to  be  as  in  the  following  table.  Comparing  them  with 
the  times  )|,  |(,  we  have  the  three  coiTections  of  the  latter: — 


Date. 

Noon  from 
Alls. 

);  anc 

i(. 

Corr. 

Mean  Time. 

Clock-cor- 
reulion. 

h     m     s 

m 

s 

t 

h     m     t 

m     s 

M.iy  15 

II     54    37 

54 

8.5 

+  28.5 

n    55    50 

+  I     13 

21 

. 

54 

7. 

.     • 

If     56      3 

I     31 

22 

. 

54 

0.5 

.     . 

II     56      7 

I     41 

23 

II     54     >8 

53 

56. 

+  S2. 

II     56    12 

+   I     54 

.  S4 

0      0    21 

59 

5&.: 

+  25.: 

II     56    17 

-  4      4 

The  mean  correction  to  the  principal  noon-mark  being  4- 25',  this  quantity  is 
applied  to  the  clock-times  of  the  transits  of  the  sun  on  the  21st  and  2  2d  to  obtain  the 
clock-times  of  apparent  noon.  The  clock-correction  for  the  time  of  the  occultation 
being  +1"'  35",  we  have: — 


38- 
29" 


37' ±i' 
1 6'. 


34  P- 


Paris  mean  time  of  occultation  of  Wkisse  II,  1656  (?)     . 
Greenwich  mean  time  of  occultation  of  Weisse  II,  1 656  (?) 

OccultatioQS  of  1690,  Apr.  13  and  July  3. 
1690.  Apr.  13.    11''  37'  52"  j'ay  vu  entre  la  fixe  derriere  le  disque  de  1»  JUine  par  la  lunette  de 

The  data  for  clock-correctious  are: — 


1690. 


h. 

;       /( 

/          // 

Mar.  24 

II 

57  48 

59  58 

»S 

58  23 

0  32 

27 

57  33 

59  41 

29 

56  21 

58  30 

30 

56  13 

58  22 

(llock  adv.  3'.  Apr. 


2 
3 
5 
6 

7 
8 

9 

10 


59    7 

I   17 

58  48*  (!) 



58  13 

0  23 

57  56 

0     6 

58    3 

0  13 

57  34i 

59  44 

57  10 



56  43 

* 

58  53 

Corresponding  altitudes  0. 

Mar.  24. 

h.    '     " 

h.  '     " 

0       / 

10    3  22 

»  55  «9 

37     0 

6  42 

5«  58 J 

37  20 

10  10 

48  31 
April  5. 

37  40 

9  38  33 

2  20    3 

38  30 

42    21 

17  14 

38  5° 

45  13 

14  22 

39  20 

49  3« 

10    I 

39  40 

52  29i 

7    3J 
April  24. 

40    0 

0  per  correspoudiug  altitudes  with- 

out correction    .    . 

SS"-  45' 

Interval   . 

....        e* 

45" 

...        >, 

t-li  Apr. 

23       •     •      II 

57    »4 

25  •     •     .      II 

57    25 

*  In  this  and  the  following  observations,  it  is  stated  distinctly  that  the  transits  are  over  the  vertical  of  the  great  quadrant. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


lay 


Clock  udv. 

3'.  Apr  12  . 

59    6 



13 

58  40 

°  S« 

»S 

57  55 

0     6 

Jiiue  II 

"  57  41 

59  58 

'3 

57  45(»>c) 

59    3 

«4 

58  25i(') 

60  44 

»S 

58  "i 

0  41 

i6 

58  " 

0  39 

July 


»i  59  '4 


59  '8 


30 
28 

3» 
35 


So  oil  Apr. 

24  the  correction  wan 

about 

+  17'. 

June  13. 

b.   in. 

// 

b.    '     " 

0     / 

9  50 

56 

284 

54  20 

53 

'9 

5  42 

54  40 

57 

4 

>  57 

55  20 

59  36 

59  25 

55  30 

10    2 

6 

June  16. 

55  5° 

li.   ' 

*/ 

b.    '      " 

0    ' 

9  22 

22J 

2    36   48 

SO  20 

24 

36 

34  32 

40 

26 

5» 

32  isi 

5»     0 

29 

8J 

29  s8 

20 

3' 

25 

27  40 
July  I. 

40 

9  27 

56 

-  -.  so 

5°  5° 

30 

12J 

SI   10 

32 

30 

5'  30 

34 

47 

5"  5° 

37 

4 

52  10 

3  Juillet  3  s  25  nne  fixe  des  Pleyades  entre 
dans  la  luiie. 


We  have  first  to  find  the  corrections  of  the  quadrant  from  the  corresponding 
altitudes.     The  results  are  as  follows: — 


Noon,  from 

From  Alti- 

Corr of 

Date. 

Quadrant. 

tudes. 

Quad. 

h     m       s 

m         s 

/ 

i6go,  M.ir.  24 

II     58    53- 

59      3-0 

+  10. 0 

Apr.    5 

59     18. 

59    30.8 

+  12.8 

•Apr.  24 

57     «9.5 

58     31.3 

+  7«-8 

June  13 

58    54.  : 

59    28.6 

+  34.6 

June  16 

59    30. 

59    32-5 

+    a.5 

July    I 

60     23. 

6o.  35.1 

+    3.1 

We  here  meet  the  perplexing  question  whether  these  great  changes  in  the  position 
of  the  quadrant  are  real,  or  whether  they  arise  from  an  accidental  error  of  a  minute 
in  the  record  of  April  24,  and  half  a  minute  in  tliat  of  June  13.  There  is  clearly  an 
error  of  one  minute  in  one  of  the  records  of  transit  of  the  sun's  limb  on  the  latter 
date:  I  have  assumed  the  error  to  be  in  the  second  limb.  But  no  change  in  the 
minutes  alone  will  reconcile  the  correction  with  the  two  following  ones.  For  Ajjiil 
24  I  have  copied  nothing  from  the  original  record;  the  transit  of  the  sun  over  the 
quadrant  was  not  observed,  but  is  deduced  from  those  of  the  days  preceding  and 
following.  For  the  con'espontling  altitudes  I  took  the  mean  of  the  actually  observed 
times  with  the  mean  interval,  the  latter  being  required  to  compute  the  correction  due 
to  the  change  in  the  sun's  declination.     The  remark  about  the  con-ection  being  +  '  7° 

. A _ .— ™^— . 

(')  J'avais  replace  le  grand  Q.  auparavant  I'observation. 


128 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


I  !un  now  (juite  unnblo  to  undcrwtaiKl.     I  Imvo  iiHsumed  tlio  correction  (»f  the  quiulrant 
to  be +12"  on  April  13  iuul -f3"  on  July  3-4.     Then,  wo  havo : — 


Date. 

i6go,  Apr. 

•3 

Apr. 

15 

July 

n 

July 

3 

July 

4 

Clock-lime  of  | 

^Joon 

. 

A 

m 

s 

II 

59 

57 

II 

59 

12 

0 

0 

23 

0 

0 

26 

0 

0 

29 

Mcau  Time. 


A 

o 


m  s 

o  18 

59  47 

3  22 

3  33 

3  44 


Clock-cor- 
ri'ctloii, 


m 
+  o 
+  o 

-t-    2 

+   3 
+  3 


J 
21 

35 

59 

7 

•5 


We  thus  deduce : — 

Clock-corrections  at  time  of  occultation 

Paris  mean  tiinen       

Greenwich  mean  times 


II' 
11' 


April 

3- 

July  2. 

+ 

24' 

+     3""    4- 

38'" 

16' 

15"     8"'  29" 

28"' 

55' 

14"  59™     8". 

The  stars  are  sui)posed  to  be  136  Tauri  and  27  Tauri. 

Assuming  the  (jnadrant  to  have  been  steady,  the  probable  errors  of  these  times 
do  not  exceed  two  or  three  seconds.  If,  howevei",  the  corrections  to  the  quadrant  on 
April  24  and  June  13  were  real,  and  the  iiistrnmeut  correspondingly  unsteady,  the 
times  may  be  in  error  by  twenty  seconds  or  more,  and  are  probably  too  great. 


Occultation  of  Aldebaran,  16^^,  Aiig.  18. 

Aug.  19,  A.  M.     I  38  44    I'etoile  touclie. 
.        .    I  39  22    I'etoile  entre. 

2  17  12    I'etoile  sorte  do  la  Inne  et  paruit  grosse. 

A  correction  of  1"'  6'  is  then  ai)plie(l  for  clock-error ;  but  it  is  not  possible  to  tell  how  it  was 
obtiiined,  and  the  confusion  of  the  observations  and  of  the  two  clocks  is  such  tiiat  the  independent 
computation  of  a  dock-correction  is  not  po-ssible.  Here,  as  in  tiiu  observations  of  1684,  we  And 
comparisons  between  a  "horloge  oricntale"  and  "horloge  occidentale  ",  but  no  indication  as  to  the 
clock  witli  which  any  ])articnh)r  observation  was  made. 

In  examining  the  observations  1686-169P,  I  Und  no  indication  that  more  than  one  clock  was 
used. 

The  last  volume  of  the  series  from  which  the  jneceding  observations  are  copied,  viz,  vol.  19, 
is  in  a  much  nicer  liandwriting,  and  is  eviilently  not  a  simple  re<.'onl  of  observations,  birt  a  mix- 
ture of  observation  and  calculated  results.  An  occultation  of  Aldebaran  was  observed  1701,  Feb- 
ruary 16,  but  it  is  hard  to  tell  what  is  meant. 

The  duplicate  series  is  bound  in  vellum,  and  is  evidently  a  simple  copy  of  the  preceding  in  a 
fairer  handwriting.  As  Ihe  copy  seemed  to  be  quite  correct,  and  to  include  everything,  [  have 
sometimes  employed  it  to  copy  from,  nearly  always,  however,  comparing  with  the  original  as  I 
went  along.  This  series  is  numbt»red  1009,  and  is  bound  in  vellum.  Vol.  i  is  missing;  at  least, 
I  conhi  not  find  it.  Vol.  2  commences  with  1682,  January  i,  but  has  no  title  whatever.  On  the 
inside  of  the  cover  of  each  volume  is  a  rude  index  to  the  principal  observations.  The  series  con- 
tinues without  interruption  to  1795,  but  a  number  of  volumes  are  missing. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


tS9 


From  Iho  iHHt  cicftorlbetl  nerioN,  v(il.  0. 

Eclipse  of  1734,  May  22  f 

ObservatioiiH  fiiiteft  par  Sarbl  (f)  daus  tour  iiifurieure  uucideiitule. 

5  55  24    com.  decl. 

6  49  10    Totalc. 
51  52    recouv.  de  luro. 
S7  40    Un  ne  voit  plus  le  Boleil. 

7  39    o    pend.  sup. 
7  39  ^^    peiid.  inf. 

Observation  falte  par  M.  des  Plages  avec  uiie  lunette  de  34  p'e<ln  pur  le  nioyeii  de  I'inmne 


du  Holeil  que  se  peiRuoit  sur  un  papier  . 
dule  a  deniie  second. 

S  56  o 
(Bio)  6  48  20 
(sic)        SI     s 


avec  une  inontre  de  poche  uiis  sur  t'beure  do  la  pen- 


coinm.  par  estimation. 
Totale. 

reuouvr.  de  lumi^re. 
Irom.  duns  I'ombre  2™  35  sec.  (sic).    Cette  eclipse  a  ^t<S  obscrvee  a  Trianon. 
A  I'observatoiie  par  M.  Gaudin.  V 

comm. 

Immersion.  "  ■        , 

recouv.  de  lumi^re. 
A  Trianon  en  presence  du  Roy. 
commencement  de  I'eclipse.  , 

ecliptie  total  qui  arriva  dans  un  instant. 

recouvr.  de  liimiere  qui  parut  conime  un  eclair,  la  pendule  avuiic'6 
de  20"  et  Versailles  est  plus  occidutitale  que  paris  de  52"  et  trlaiioa  est  encore  a  I'occid.  do  quel- 
ques  sees. 

All  this  is  a  literal  copy  from  tlie  record. 

The  transits  of  tbe  sun  were  as  follows: —  * 


s 

ss 

16 

6 

43 

S' 

s» 

13 

S 

54 

SO 

48 

»4 

5° 

40 

)l 

58  44      3'  adv.  k  la  pend.  superieur. 
I  39  Bon. 
«  36 

1 37  ,;■  •■"■^^'    ■. 

I  31 


l( 
Mai  21     II  56  28 

22  59  22J  Dontcux. 

23  59  15  a  |)eu  [ires. 

24  59  23 

25  59  J9 

26  59  19 

Tbere  are  110  altitudes  till  December  30,  aiul  then,  it  would  appear,  only  because  something 
had  happened  to  the  quadrant. 

From  this  point  onward,  the  observations  are  made  and  recorded  too  carelessly  to  be  of  any 
use.  A 

Eclipse  of  1715,  May  2.8. 

•    3  May.  el's!'    o"  pend.  sup.  ' 

6   50'  54"  pend.  inf. 
»<>'M"  8   i^     o    comm.  de  I'Eclipse.  lunette  de  8  pieds,  pend.  iuf.  et  lunette  de  34  pieds. 

3  Doits  • 

5'1-i 

6  '■■■    -^v-'v  --':■ 

10  d.  i  (sic)  '     ' 

II 
II 

6 
4 
17- 


8 

13  0 

8 

27  30 

37  20 

41  30 

45  50 

9 

18  IS 

20  12 

40  SO 

53  0 

0 

II  30 

■75  Ap. 

'30 


RESEARCHES  ON  THE  MOTION  OE  THE  MOON. 


17  16 
23  o 
28  30 
»2  33  ° 
32  55 


t 

I 


Fin  obHorvt'«5  u  luiioite  (!«' 8  [litMlM. 
Iioiitl.  Hiip. 
pciitl.  inf. 

OliHcrvntion  f'aito  11  Miirly.    (Uoconl  in  the  Haino  hand,  and  that  u  gouti  one.) 
Le  2.  May  a  9''  14'    6"  H.  <l.  Arcturns  51  40 


9  19  10 
Lc  3.  May  a  6  40  52 
II  32 
16  10 
20  58 
26  49 
«9  54 
a    o 

38     7 


52  20 
II.  (In  0  18  30 

a  8    II   32    Cnnunenucment  vu  avoo  une  lunette  de  8  piedH, 
s    16   10    Un  doit.      Le  peiidule  a  avanc^  de  30"  qu'il  fiiut  retrancher  do 
2  [touteH  km  olmervations. 

3 

I 

4  ■■      .  ■  . 

Qiiatre  doits 
Ginq. 

lOniitted  copying  the  rest  of  the  observations.  They  are  found  printed  in  the  Memoirs  for  1715.] 
lo""  28'  20"  Fin,  qne  I'antres  personnes  ont  jugeiSs  a  lo*"  28'  o" 
10   34  59    H.  dn  0  52  40. 

Le  Roy  a  assist*!'  aux  observations  qui  se  sont  faites  vers  le  milieu  et  a  In  flu  anssy  blen  que 
M.  le  Due  d'Orluans  et  toiUe  la  cour  qui  y     .     .    .     pendant  presque  toute  la  dure6  de  I'Eulipse. 

At  the  end  ot  the  volume  is  given  the  ciilcniiition  of  clock  error  from  the  four  observvd  alti- 
tudes, A  ;.  Areturus,  210°  42'  31,";  of  ©  at  noon,  38°  55'  33";  at  time  of  observation,  39°  17'  36". 
Altitude,  5'°  40' o" -48"  =  51°  39'  12";  y  =  90°— 41O8' 25";  H  =32038' 24"  &.  31  22  54;  set. 
deh  o'  57"  (f)  o  58"  (f).  . 

J'ay  avance  lu  pend.  d'une  minute. 

Next  morning  clock  errors  -   37"  &  —  28".     N.  P.  D.  Arcturus  69°  19'  8". 

There  is  no  clue  to  the  phvce  wliere  or  the  jjerson  by  whom  the  first  of  the  above 
set  of  observations  was  made,  except  the  dock-error,  wliicli  agrees  with  one  determined 
at  the  Paris  Observatory.  The  second  set,  made  at  Marly  (now  Marly-le-Roi),  agrees, 
so  far  as  I  copied  it,  with  the  printed  observations  in  the  Memoircs  The  presence  of 
the  monarch  probably  exerted  a  very  injui-ions  effect  on  the  observations,  and  I  have 
been  in  some  doubt  whether  they  are  worth  using. 

For  clockcoirecti  ;n  at  Paris. 
1715.    May  I.  A.  M.  8  5   i6pen.  inf.  =  8   11   o  pin.  sup.,  Diff.  5' 44". 


I 

II 

59  26 

(         «38 

)l 

a 

5921 

I  33 

3 

59 '8 

«  30 

Now 

comes  this  calculation 

:— 

.• 

II 

5918 
I    6 

12 

0  24 

33 

midy  pend. 

II 

59  51 

sup. 

11 

5946 

midy  pend. 

inf. 

May  1. 

H.  ci' Arcturus 

1. 

S"    8' 42" 

41"'  20' 

8    22  33 

43   30 

8    25  42 

44     0 

8    29     0 

44   30 

8   32   «S 

45     0 

8   35  36 

45   30 

8    38   52 

46     0 

8  42   15   epy 

26    20 

46     5 

26   40 

9  46    4    le  petit  cbien 

»3   30 

59    9 

13     0 

2   12 

12   30 

14"  a  ad. 
4  May.  1 1  59  18    |(        1  30    )| 
The  record  gives  no  means  of  judging  which  clock  was  used  in  observing  the  altitudes,  or 
when  the  pend.  inf.  was  put  back. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  I3I 

Tlio  coiiicidonco  <tf  clock- errorn  leaves  no  doubt  that  wo  here  Imve  tlie  clock- 
correction  tor  the  unidontiticMl  oI)8ervutioii  iit  tlie  I'liris  Obwrviitory.  T  make  the  cor- 
rection lor  qnadrunt  —39"  iiiHtead  of —  33",  and  find,  for  tlio  correction  to  reduce  tlie 
^^pnnl.  inf."  to  mean  t.nio,  —  3"'  2".  'Phis  will  make  the  time  <tf  hefrinniiifr  58"  later  than 
that  observed  by  La  IIikk  and  the  others,  a  ((nantity  so  <rreal  ;is  to  lead  to  the  sus- 
picion of  a  inistake  of  a  minute  in  the  record.  The  end  a<(rees  well  with  that  observed 
i)y  the  La  Hires.  The  observations  of  dij«its  are  too  wild  to  merit  consideration,  and 
altogether  it  does  not  seem  worth  while  to  make  any  further  use  of  these  observations. 

8ERIKB  II.  ; 

ObnefvatiouH  0/ La.  UinVu 

In  this  series  of  observations,  the  dock-errors  are  more  carefully  determined  than 
in  the  case  of  the  observations  of  the  (Jassinis.  ( )ccultatif»ns  are  found  only  in  a  few 
widely  scattered  years  between  1682  and  1718,  but  the  times  are  so  well  determined 
that  they  seem  to  compare  favorably  with  modern  occnltations  in  precision.  The 
transits  of  the  sun,  and  occasi(»nally  of  stars  and  planets,  are  observed  over  some 
meridian  instrument  which  does  not  seem  to  have  been  disturbed  while  La  Hire 
used  it.  The  foUowinj^  are  the  con-ections  ner-essary  to  reduce  the  times  of  transit 
over  the  instrument  to  those  over  the  true  meridian  as  derived  from  the  corresponding,' 
altitudes  of  the  sun,  which  are  found  in  the  following  i)ages : — 


Date. 

1684,  July 

10 

Dec. 

>9 

1685,  Feb. 

13 

May 

28 

July 

16 

Sept. 

M 

Oct. 

10 

Oct. 

117* 

Nov. 

27* 

l6gq,  Juno 

2» 

Aug. 

21 

Sept. 

13 

Oct. 

23 

1706,  May 

6 

1708,  Sept. 

16 

1715,  May 

9 

CUick-tin.e 
of  Transit  of  "1 

over  Mcrid. 
of  Instrument. 


A 

12 

12 

12 

II 

o 

o 

o 


s 
23-<' 
43-8 
28.0 
50.0 

7.8 
58.6 

2.q 


o 
o 
II 
o 
o 
II 
II 


1.8 
4.0 
A-5 
17.2 
16.5 
38. o 
26.0 


.Mean  '"lock- 
time  off  orres. 

Al'.ituiics. 


// 

12 

lU 

12 

II 

O 

o 

o 


;;/ 
5 
9 
6 

59 
o 
4 
I 


s 
32.8 
28.2 
32.0 

9-9 
12.2 
30.4 
28.6 


o  52.3 

57  42.0 
59  41-6 

o  39.6 

58  9.7 
58  49.2 


Mean 


Corr.  for 


Interval.    Mot.  of  0. 


'" 
50 
22    I 
32 

«3    ! 
o 

54      ; 

16  ' 


s 
+     6.0 

+  03 

—  19.0 

-  6.6 
+  9-8 
+  20  9 
+  21.3 


27 
I 
34 
3' 
49 
20 


+  I5.3 

+  18.7 

+  20.7 

-  13-5 
+  21.0 

-  13-5 


Transit  of 

0  over  True 

Meridian. 


Corr.  of 


///       s 

5  38.8 
9  28.5 

6  13.0 

59       3-3 

0  22.0 

4  51-3 

1  49.9 


Merid.  In-  ;    Dec.  of  0. 


strunient. 


20.0 
7.6 
0.7 

2.3 
26.1 

58     30.7 
58     35-7 


-t-  15-2 

-  '5-3 

-  15.0 
+  13-3 
+  14-2 

-  7-3 

-  13.0 

-  16.2 

-  15-2 

+  18.2 

+  3-6 

-  3-8 

-  14-9 
+  9.6 

-  7-3 
+  9-7 


+  22 

-  23 

-  13 

+  21 

+  21 

+  3 

-  6 

-  13 

-  21 
+  22 
+  12 
+  4 

-  II 
+  16 
+  2 
+  17 


15 
26 

26 
25 
29 

35 


*  For  these  three  dales,  I  have  accepted  La  IIirk's  reduction  of  his  corresponding  altitudes,  as  his  reductions  were 
found  in  other  cases  to  be  correct. 


132 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


We  now  arrange  these  con-ections  according  io  the  sun's  dechnation,  putting  in  a 
separate  cohimn  those  determined  after  the  interval  of  14  years  between  1685  and 
1699.     We  find  them  to  be  as  follows: — 


)'8  Dec. 

1684-5. 

1699-1715. 

Porninla. 

0 

a 

a 

I 

a 

-23 

-15-3 

. 

-157 

—  21 

-'5-2 

• 

—  16.I 

-13 

-15.0- 

16.2 

* 

—  14-9 

—  XI 

» 

-  14.9 

-14. 1 

-    7 

-  13-0 

'  * 

—  1 2.6 

+    3 

-    7-3 

-    7-3 

-    66 

4 

• 

-    3.8 

-    5-7 

12 

■■»■ 

+    3.6      . 

+    2.7 

16 

* 

+    9-6 

+    8.0 

n 

. 

+    9-7 

+    90 

'>i 

-^-^3^3  + 

14.2 

. 

+  I5-I 

2^ 

+  15.2 

+  18.2 

+  16.6 

There  seems  to  be  no  evidence  of  any  change  in  the  instrument  during  the  whole 
period  of  the  o]3,servations.  Supposing  the  axis?  on  which  it  turned  to  be  qtiite  true, 
so  that  its  deviation  from  the  meridian  arose  only  from  errors  of  level,  collimation, 
and  azimuth,  the  correction  nee  essary  to  reduce  the  time  of  transit  of  an  object  over 
it  to  the  true  meridian  could  be  expressed  in  the  form 

m  -\-  c  sec  S  -\-n  tan  6, 
6  being  the  declination  of  the  object.     The  values  of  the  constants  which  best  repre- 
sent the  above  deviations  are: — 

ni=:  —  i2i'.4  i 

c  =  -}-  ii2".7  I  r 

n  =  +    39'.8.  ! 

The  nunibers  computed  from  these  values  of  the  constants  are  givca  above  in  the 
last  colunni  They  seem  to  represent  the  observed  deviations  within  the  probable 
errors  of  the  observations.  'J'he  following  table  shows  the  corrections  computed  from 
the  formula ; — 


Decl. 

Correc- 
tions 

Diff. 

s 

s 

-   25 

-   15.8 

—  0. 1 

—  20 

-   15.9 

+  0.6 

-  15 

-   '5.3 

1.3 

—  10 

—   14.0 

2.2 

-     5 

—   II. 3 

3.1 

0 

+     5 

-  8.7 

-  4.8 

3.9 
4.8 

10 
15 

0.0 
+     5.9 

5.9 
7.0 

30 

+   12.9 

+    8.7 

S5 

+  21.6 

We  shall  use  this  table  in  reducing  transits  to  the  true  meridian  in  order  to  obtain 
clock-con'ections. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Extracts  from  La  Hire's  Journal. 

Vol.  93,  page  4. — La  Hire's  first  occultation,  observed  at  Observatory. 


m 


1682,  Feb.  15. 2- 

Mane. 
9     I   49 

'7  3^ 

Vesper. 

2  58  40         Correct.  37^^. 

11  etoit  done  inidy  a  1 1  59  55 

964 

18    0 

51  23>4 

.  :. 

9   10   24 

18  30 

5°    2 

Le  17  a  midy  I'horloge  de.oit  se  tarder  de  37. 

From  altitudes  of  Cauda  Leonis  it  seems  the  clock  lost  28""  52'  on  sidereal  time  between  Feb- 
ruary 10  and  17,  or  11"^  a  day  on  mean  time. 

Tbe  following  are  the  altitudes  on  the  17th  : — 
1682.  Feb.  17. 


4'    6" 

Alt. 

=  28°  30' 

7    II 

29      0 

10    15 

29    30 

13    22 

30      0 

Doub.  * 


Eclipse  of  Hyades  par  la  Inne  Feb.  15. 
6  59     2     Emersion  of  «.  (  According  to  Le  Monniek,  Hist.  Coelente  p.  257,  the 
'<  h.  »         appai 


(    6  59     2 
J    7     I  27 


apparent  times  were  6  59 


7   I  37- 


The  corresponding  altitudes  of  the  sun  give: — 

Clock-time  of  ©'s  transit 23"  59™  54".9, 

While  mean  time  of  0's  transit  is -o''  14™  41". 7. 

Clock-correction        +  14"'  46".8. 

The  clock-rate  being  1 1'  5  per  d-iy,  the  error  at  the  time  of  occultation  would  be 
-f  14"'  50".2.  As  a  check  upon  thj  rate,  I  have  computed  the  correction  from  the  alti- 
tudes of  /?  Leonis  on  February  1 7,  and  found,  as  the  mean  result  from  the  four  alti- 
tudes : — 

Feb.  17,  9"  9'"  clock-time;  correction  =  -f  15'"   io".5. 

This  gives  a  rate  of  10"  i)er  day,  and  a  ("orrection  at  the  time  of  occultation  o".4 
less  than  that  found  above.     I  have,  however,  used  +  14"'  50^.2,  giving:— 

«|  Tami.  «'  Taiiii. 

Paris  mean  times  of  occultation       .     .     7"   13'"  5  2".  2         f   16"'  17".  2 
Greenwich  mean  times  of  occultation        7"     4""  Si'- 2         7"     6"'  5 6". 2. 

The  equation  of  time  being  +  14"'  40".8,  these  result,s  do  not  differ  one  second 
from  those  given  by  Le,  Monnikk.     The  phase  is  actually  immersion,  not  emersion. 

©  Eclipse,  1684,  July  12. 

Manuscript,  vol.  93,  page  287.— Observations  of  La  Hire. 

10  Julij. 

Altitudines  superioris  Limbi  ©  pro  horolog. 


Mauo. 

7  32  S4i 

31°     0'     • 

35  58 

31     30 

3S'    8"    Correctio  i2.i  addenda 

38  59 

32       0 

32     si 

42     3 

32     3° 

29     2 

45     5i 

33      ° 

4  25    59i            . 

134  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Meridies  Inrologio  indicante 12''  5'  38" J 

0  Traiisiti  8  i)rioris  Liiiibi       12    4    15^ 

Traii.situs  posttTioris  LiiuUi 126'  32" 

•■    •'  '  ■  2  i6f 

Transitns  centri 12  s  23g 

Traiisitus  per.  ver  Meridianuin 12  5  37 

5   Traiisiius  eeutrl 3h  6  32^ 

Traiisitus  veri  Temp,  per  vernui  Merid.    ...-...,.  3  o  55 

U  Traiisitus  Centri 4''  i'    8" 

11  Julij,  :    , 

0  Transitus  prioris  Liiiibi      12'"  4'  19" 

TrausituB  posterioris  Liuibi 12    6   35^ 

■                 .  '      2  16J 

Traiisitus  centri 125  27J 

Altitude  Merid.  suiierioris  Liiiibi 63  27  50 

N  Serpentarii  Traiisitus 9  30  54J 

et  tardavit(?)  liorologiuin  pro  duobus  diebus io"J 

12  Julij. 

Altitudiuos  superioris  Limbi  0  pro  borolog. 

Manu. 
5  36     5  21°  30' 

39     H  22       o 

42    14  22     30 

45  ^^         23    o 

Vespere  Eclipsis  Solaris. 

Plinses.  TenipuH.  I'LiiHcs.  Tempus. 

29'  56"  2"  3S'  59"  II'     5"  3"  45'  49" 

27    51  41    49  12    45  56    49 

27    13  43    59  13    45  42    29 

24    ss  49    59  14    39  69 

23    36  53    49  16    14  10   49 

22   '4  57    29  19    32  19-  39 

19    55  3       3    49     ,  21    23  24    19 

17    56  9    59  23    36  30    39 

16    14  16    29  .         26    46  37    39 

14      I'  23    49  29    37  44    19 

13      4     ,  .     27      9 

It    48  34     9          Initiuin  2    31      6      tempore  borolog. 

no  42      9  5    42  J    corr.  horol.  aubt. 


Chordae. 

Tempiia. 

13'  3°" 

2''  38'   19" 

17      5 

45    49 

21      IS 

55      9 

22    s° 

3       0    19 

25    49 

7    49 

26    27 

13    34 

27    13 

19    19 

28    34 

29    39 

29    37 

37    39 

28    24 

59    19 

25    23i 

temp. 

vero. 

Cliordae. 

Tenipiig. 

27'  IS" 

4"    8'   i6' 

23    55 

22      19 

22    20 

26     39 

19      5 

34      0 

12    45 

43      9 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Fitiis  totiiia  Eclipseos,  4''  49'  9". 

Pars  illumiiiata  17'  44",         4''  14'  49"  Ditim.  Ltinae  29'  39." 

Horologiuin  acceleralmt  tempore  Eclipseos  5'  42"^. 

Fiiit  igitur  flnis  veri  temporis  4''  43'  26"^. 

13  Julij. 
Altitndines  snperioris  Limbi  0  pro  horologio. 


135 


Mane. 

8  33   12 

40O  30' 

3  38    S 

Coirecitio  addenda  12" 

36   >9 

41       0 

34  58 

39  28J 

41     30 

3>  49 

4»  37 

42       0 

28  40 

In  meridie  sole  cxistente,  horolog.  indicavit  12  5  44  J. 
The  clock-corrections  for  this  eclipse  are  derived  as  follows : — 


The  single  altitudes  observed  on  the  morning  of  July  12  could  be  made  avail- 
able for  detennining  the  clock-con-ection  on  that  day  ;  but  the  rate  of  the  clock  is  so 
good  that  I  have  not  deemed  it  necessary  to  go  through  the  labor  of  discussing  them. 
Interpolating  between  July  1 1  and  13,  we  find  for  the  clock-error,  before  and  after 
the  eclipse: — 

July  12,  2^.1 Clock-correction,  — 42^o. 

July  12,  5^3 Clock-correction,  — 4i'.o. 

Occultation  of  /j.  Oeminortim,  1684  December  21. 
19  Deceinbris  Mane  HE  Transitus T*"  25'  7" 

Alt.  ©  sup.  limbi  pro  horolog. 

Mane.  Vespers. 

a*  S3'  55"  6°    o'  25™    2'           i"  corroctio  add. 

56  54  6    20  22       2 

'59  SS  6    40  19      2 

9      2  57  70  3  IS    59 

Oeutrum  0  trafisivit  per  nicrid.  indicante  horolog 129  28^ 

9  Trans'ius  centri 96  55J 

0  Trau.  prior,  limbi 12    8  33 

"      posterioris  " 10  54 J 

"      centri       129  433 

Ceti  08.     transitus      . 90     i 

Aldebaran      "  '°  3'    37 

3)  I  "  10  33   46 


136 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


20  Decembris. 

Betroactuiu  est  borolog.  Io^ 

®  transitus   I    11  59    o 

"        "         II     12    I  22 


Cent.     12    o  II 

21  Decern  bris. 
Ceti  08.  transitus  8  42  4. 
Pro  dnobus  diebns  tardavit  horolog.  5". 
Inter  '21  et  22  in  media  nocte  accelerav  horo!.,  33". 
Accelerae  lior.  in  media  nocte  37". 

Vespere. 

Occultatio  stellae /i  II         (i^'r^e  eclipsata 93523 

Einersio  vel  apimr.  ejus    •  10    9    2 

Transitus  Dl     ....  121  44^ 

II 12    4    o^ 

2  Decembris. 

0    1        II  S9S3i  ; 

O  II        12    2  16  : 


16 

8 


Cent.        12    I    4| 

The  clock-corrections  derived  from  the  transits  of  tlie  sun  fi-oni  December  19  to 
22,  and  tliose  of  the  moon  and  a  Ceti  on  the  21st,  are  shown  in  tabular  form  below. 
The  first  transit  of  the  sun  is  that  derived  from  the  corresponding  altitudes.  The 
tabular  right  ascension  of  the  moon  probably  requires  an  increase  of  two  seconds  of 
time;  this  correction  has  therefore  been  applied  to  its  tabular  right  ascension  at  the 
time  of  transit  to  obtain  the  mean  time  of  ti'ausit. 


Date. 

Object. 

Clock-time  of 
Transit  over 
Meridian  In- 
strument. 

Corr.  for 
Deviation. 

Clock-time 
of  Transit 
over  True 
Meridian. 

Computed 
Mean  Time 
of  Transit. 

Apparent 

Clock-cor- 

tion. 

1684. 

A     m        s 

s 

m        s 

m         s 

m       s 

Dec.  ig 

©    .      .      . 

0       9     43.8 

-     15-9 

9    28.5* 

58     19-3 

—   M      g.2 

20 

©    .      .      . 

0      0     II. 0 

-     15.9 

59     55-" 

58     49-4 

-     I       5.7 

21 

n     Cell      . 

8     42      4. 

-       6.3 

41     57-7 

40    53-8 

-     I      3-9 

21 

Moon  . 

12       2     52.5 

-1-     I7-0 

3       9-5 

2        6.0 

-     I      3-5 

22 

©    .     .     . 

12       I       4.8      —     15.9 

0    48.9 

59     49.8 

-    0    59.1 

The  occultation  was  observed  between  the  transits  of  a  Ceti  and  the  moon.  The 
agreement  of  the  clock-corrections  and  the  uniformity  of  the  rate  seem  to  indicate 
that  the  times  can  be  determined  within  a  second.  Deriving  the  clock-correction  from 
the  transits  of  a  Ceti  and  the  moon,  we  have : — 

IiGmersion. 

Clock-corrections  for  occultation  of  /i  Geminorum  .     .       —  i"    3".8 

Paris  mean  times 9''  34™  i9'.2 

Greenwich  mean  times 9''  24'"  58'. 2 


Emersion. 

10"    7'"58'.3 
9"  58"  3r.3- 


^From  the  corresponding  altitudes. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


137 


1685,  Feb.  13. 
Altitudiiies  sup.  limb.  O  pro  hor, 

Mune.  Vespere. 

8"  46'  14"  14O  20'  26' 51" 

48  S3  14    40  24  10    Correct,  subt.  38". 

SI  34  IS      o      ^  21    29 

54  17  'S    20  18  48 

iSolis  ueut.  tetigit  moridianuni,  iiidicaute  bor.  12  6  13. 


O  transitus    I 
II 


7  3S 


Centri  12  6  28 

On  1684,  Dec.  2,  the  transit  of  ©  was  i4>4"  late,  so  that  there  can  be  no  doubt  of  the  correc- 
tion to  La  Hire's  guonion. 

Here  there  is  a  lacune  in  Delisle's  copy  of  La  Hire,  from  which  the  preceding  is  copied ; 
this  lacune  is  afterward  filled  up  from  La  Hire's  original. 

1685.    For  correction  of  La  Hire's  meridian. 

P.M. 
34029     i3j"corr.  subt.      ©Tr.  115742 


A.M. 

Mfty  28 

8  17  so 

39    ° 

20  S7 

39  30 

24    4 

40    0 

27  iij 

40  30 

6  20  56 

24    2 

39  3° 

7  3*34 

35  45 

3856 

42    6 

7  18  42 


7  48  21 

5'  44 
55  "^ 
583s 


July  16. 

19  30 

20    0 

22  30 

Sept.  14. 

17     0 

'7  3° 

18    0 

1830 

Sept.  13. 
15  ° 


Oct.  10. 

12  o 

30 

13  ° 
•3  30 


37  22J 
34  '6 
3'  9 


n  59  58 

II  58  5° 
over  mer.  1159  3 


5  39  2<5  J 

!I   ) 


.  21"  add. 
36  21 

20  s8   19"  add. 


+  13" 

©  Tr.  II  59  oi 

12  o  16 


12  o  73 


43626  42"  add.   Sept.  13O  19  426 

33  "6  J2  6  34 

30  6  _.  

^^^55  4,"  add,          '='5  3° 


per  ni. 


s  214 

8A 


45118      43"  add.      Sept.i6©   12    2  51^ 

S    ° 


12    3  55? 

4  1438        ,    .,,■,       Oct.9,  ©tr.  12    I  22i 
...3       "^^^  332 


4  23 


12  2  27J 

Oct.  II.  O  tr.     12    o  325 

2  42* 


18- 


-75  Ap.  2 


12    I  37J 


t58 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Vol.  93,  p.  429. 
Iiniiiei-sio  stellae  H  Geiiiinoruin,  1685,  Oct.  17.    9  52  29  Penil. 

Oct.  16     ©  cent,  transit         11     59     38 

17  Sclieat  Fegiisi  tr.      9     14     11 

Markab.  9     15*  57     [•  Le  Monnier  prints  14,  which  is  rinht,  but  it  is ck'aily 

18  a  Aquilai  5     57     45  15  in  the  MS.] 
Scheat  Peg.              9     "o      S 

Markab.  9     10    51 

20     0  II     58     16.6 

27    Correction  of  qnadrant  per  ©  —  i6'J. 
Nov.  27  "  "  —  iS'i- 

The  clock-corrections  from  1685,  October  16  to  October  20,  are  derived  from  the 
observations  as  follows : — 


Date. 

Object. 

Dec. 

Corr.  for 
Deviation. 

Clock-time  of 

Transit  over 

True  Meridian. 

Computed 

Mean  Time  of 

Transit. 

Apparent 

Clock-cor- 

tion. 

C. 

A. 

1685. 

0 

s 

h      III         s 

A     III         1 

m        t 

s 

s 

Oct.  ifi 

-     9-3 

-     13.8 

II     59     24.2 

23     45     31.2 

-  13     53.0 

53.0 

0.0 

17 

a    Pegasi. 

+   26.3 

+     23.9 

9     14     34-9 

9      0    48.5 

-   13     46.1 

39- « 

-    7-2 

a     Pegasi  . 

+   13.5 

+       4-0 

9     15       II 

9      I     20.4 

--   13     40-7 

39-2 

-  1.5 

18 

1     Aquilx. 

+     8.1 

-       '-9 

5     57     43.1 

5     44     14-4 

-  13     28.7 

30-5 

+  1.8 

li    Pegasi  . 

+  26.3 

+     23-9 

g     10    28. g 

8     56     52.0 

-  13     36.9 

29.2 

-   7.7 

a    Pegasi  . 

+   «3.5 

+       4.0 

9     10     550 

8     57     23.9 

-  «3    311 

29.2 

-   1-9 

20 

©    .     .     . 

-   10.7 

-       14. 2 

II     58       2.4 

23     44     49.4 

—  13    13.0 

13.0 

0.0 

The  discordance  of  clock-errors  is  perplexing.  There  is  a  seemingly  systematic 
difference  of  nearly  six  seconus  between  the  corrections  from  a  and  from  /3  Pegasi. 
As  the  latter  lies  without  the  limits  between  which  the  deviation  of  the  instrument 
was  determined,  the  corresponding  result  is  to  be  received  with  suspicion.  If  we 
determine  the  clock-correction  and  rate  from  the  transits  of  the  sun  on  the  16th  and 
2 1st,  we  have  the  results  in  colunms  c'  and  A,  the  latter  being  the  dif/erence  between 
the  computed  error  and  that  dei'ived  from  the  intermediate  observations.  The  most 
probable  value  of  A  for  the  tinu  of  the  occultation  may  be  estimated  at  — I'.o,  with  a 
probable  error  of  2".     This  .will  give  for  the  occultation  of  H  Geniinorum: — 


Clock-correction 

Paris  mean  time  of  the  occultation,  October  1 7 
Greenwich  mean  time  of  the  occultation  .     .     . 


13" 
38" 
29^ 


4g'.o 
49".o 
2810  ±  2'. 


Mane,  19  Augnst  1699. 
Imniersio  Aldebarau     i"  41""  36' 
Eiuersio  2    19     37. 

Sed  etiain  in  iiiunienio  apimiuit  niagna'et  in  disco  d  reflexionc  luniinis  tei 

The  observed  tninsit.s  of  0  were: — 

Ang.  15  II  57  38 

'7  58  23 

18  58  43 

"  59  .S9 


rae  illnstratiie. 


U. 

59  48J 
o  33 
o  54 
2     9 


Cent. 

58  43i 

59  28 
59  48i 

I     4 


A.  M.  Aug.  19  ^       o  14  17 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON, 


139 


Aug.  21. 

Altitudines  0 

pro  liorolog. 

8  II     I 

30  30 

3 

S°  43i 

14  14 

31     0 

47  30 

17  28 

31  30 

44  18    (Joir.  3 

20  39J 

32    0 

41     4i 

23  S° 

32  3° 

37  48 

L^iitrmn  ©  perveuit  ad  Oiroulem  lueridinniiiu  iiidicmite  lioroIo;;io  12''  i'  7"^. 
Qiiivre  tiirdiit  qiiiidrmis  munilis  in  altitudiiimn  53°  12'  ...  .  3 J". 

On  tlie  2d  June  preceding,  he  found  iv  coneotion  to  tlie  quadnmt  of  +i8"4,  as  follows:  — 
0  Tmnsit June  i,    o  i  48 

5.    °  2  55 
Debui  transire     ....      "    2,    o  2     ijj 
Transit  per  alt.  corresp o  2  20 


Corr 


+  i8i 


Again,  Sept.  12,  tlm  correction  w,is  —4".    Tlio  change  prohibly  ilependa  on  the  sun's  Z.  D. 
The  derivation  of  clock-corrections  from  transits  of  the  sun  is  as  follows : — 


Clock-time 

1 

Date. 

Dec. 

Corr. 

of  Transit 
over  True 

Mean  Time. 

Corr.  of 
Clock. 

Hourly 
Rate. 

Meridian. 

I6g9, 

0 

.f 

/(    m       s 

A     m     s 

■ 
m    s 

s 

Aug.  15 

+   14-0 

4- 

4-7 

II  58  47-9 

0    3  55-9 

+  5     8.0 

1.42 

17 

13-4 

4.0 

59  32.0 

0     3  31.8 

3  59-8 

1-37 

l3 

13.0 

3-4 

59  5"-9 

0     3  18.9 

3  27.0 

1.62 

2t 

12.0 

4- 

2.2 

61     7.2 

0     2  37.5 

I  30.3 

In  obtaining  the  time  of  the  last  transit,  double  weight  has  been  given  to  the 
result  from  equal  altitudes.  Interpolating  between  the  last  two  corrections,  we  liave; 
for  the  times  of  phases  : — 


Clock-correction 

Paris  mean  time,  1 699,  August  1 8 
Greenwich  mean  time      .... 


Irameraion. 

+  3""  4'-8 
i3''44'"46'.8 
I3"35™i9'.8 


EnierBion. 

+  3"°  3"-8 
14"  2  2 '"40".  8 
i9».8. 


14"  13 


Initium 

8i'i3'  18" 

Dig.  oj 

IS  43 

I 

18  28 

14 

22   19 

..•  a 

25  3° 

-  .  -»*- ■ 

28  44 

i 

30  46 

it 

34  19 

4 

37     6 

4i 

40     4 

S 

43  «6 

Si 

46  55 

23  Sept.  ©  Eclipsi.**,  1699,  luaue. 
Dig.  8  30 
8  o 

7  30 
6  30 
60 

;-:-       5  3° 

.-.     ,  5     ° 

4  30 

'    :      ■       40 

*i  3  30 

30 

2  30 


41  39 

45  37 

49  27 

55  42 

o  16 

4  13 

9  S 
12  47 

15  55 
19  6 

23  5 
27*  4 


•  It  seems  as  if  the  minutes  first  recorded  were  26,  and  that  they  were  afterward  changed  to  27.  There  is  no  evidence  10 
show  with  certainty  whether  this  was  simply  to  make  the  ditferences  run  more  smoothly  or  not.  The  change  was  evidently 
made  after  taking  the  differences. 


140 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Dig.  6 

8"  so' 28" 

6J 

54     2 

1 

57   23 

7  a* 

9     I   20 

8 

5  " 

8  30 

9  12 

9 

14     6 

Ditiir 

93* 

21   21 

MHxiriia 

obsciiritiw. 

Teiiii 

9  3° 

28  57 

9    » 

35  S3 

0  tr.  I. 

II. 

Cent. 

Sept 

12 

II  57     0 

59     9 

58     4i 

13 

56  35 

58  43 

57  39 

II 

57  27 

59  39 

58  31 

20 

58  3oi 

o38i 

59 

21 

.      • 

0  i6i 

59  114 

22 

57  45 

59  524 

58  48.? 

23 

57  20J 

59  29 

58    24.={ 

26 

56    8 

58   17 

57  «2i 

Oct, 

22 

59     8A 

I   20J 

0  i4i 

23 

59  " 

I   23J 

0  i7i 

24 

59  14 

I  26 

0  20 

Oct. 

23 

Cent.  0  tr.  per  iner.  circ. 

ind.  horol 

12 

0     ij 

Dig. 


2    0 

10  30  26 

I  30 

33  S3 

I       0 

37  '9 

0  30 

39  57 

flni8 

43   '8 

Diiimeter  0  cum  micrometro  31'  58". 
Tempore  observaliiiiiis  liorolog.  tanlebat  i'  41' 


Sept.  12. 
Altitudines  0  pro  borol.  et  qua- 
(irantis  muralis  deviatione. 


8"  12' S3" 

25"  0' 

42'  30" 

22  s8 

26  30 

32  26 

26  20 

27     0 

29    3 

29  47J 

27  30 

25  37 

33  15 

28     0 

22     9 

36 '44 

28  30 

3   18  42 

363 


Oct.  23. 


37  20 

70  0'            22     2 

40  46 

7  30       18  i^ 

44  15 

80       15  7 

47  45 

8  30         4  II  4« 

Oorr.  40 J  add. 

Quamobrem  aufernndum  iu 
mnralem. 


baec  altitudiue  0  15"^  a  traiiaitti  0  centre  per  quadrantem 


The  clock-coiTections  are  derived  thus  : — 


Date. 

Clock-time 

Mean  Time 

Clock-cor- 

of Transit. 

of  Transit. 

rection. 

1699. 

h    m       s 

h    m      1 

m       s 

Sept.  20 

23  59  26.2 

23  53    9.3 

—   6     16.9 

21 

59    3-0 

52  48.6 

-  6     M.4 

22 

58  40.0 

52  28.0 

—   6      12. 0 

23 

58  15.8 

52    7-5 

-  6      8.3 

26 

57     2.8 

51     7-0 

-  5     55-8 

The  correction  for  the  time  of  the  ecHpse  is  —  6"  9'. 

.    *  1701,  23  Sept.  (mane). 

Aldebaran  occultata  a  Luna  6  10  50 

670  veri  temp. 
Notandum  quod  stella  jam  supra  discum  Lunae  quaiititatae  i^  diainetri  suae  apparebat 
quando  oninino  evanuit,  et  circiter  post  2"  temporis  ceiitri  stellai'  iminersiouis  apparentis. 
(A  similar  lemark  was  made  on  the  other  occultation.) 
Emersio     .    .     6  57     8 
Veri  temporis     6  53  18.    L'horloge  tarde  de  35"  par  jour. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


I4I 


There  are  no  corresponding  altitudes  given  since  those  of  Oct.  23,  1669,  but  he  seems  to  know 
the  errors  of  his  quadrant  e.  g. 

20  Sept.  1701  9  centri  Transitus  per  Quad.  mur.    11''  7'  42". 

Trausitus  per  Q.  M.  veri  temporis  II  2  12^    altitudo  ver.  50°  n'. 

Transitus  per  V.  merid.  ver.  temp.  II  2  12. 

On  the  same  day  we  find  : — 

Trausitus  centri  ©  per  vero  inerid.  12  5  28,  indicating  a  correction  of  —  6". 


Sept.  23  per  ver.  merid.  12  3  41. 


© 

tr.  1. 

II. 

Cent. 

1 701,  Sept.  19 

12 

S     7J 

7'  16" 

6   llj 

20 

4  30 

6  38 

5  34 

21 

3  35 

6    3 

4  59 

23 

*  43 

4  5« 

3  47 

*4 

2     8 

4  16 

3   '2 

There  are  no  altitudes  within  the  two  years  following,  aud  no  explanations  of  the  data  for 
deviation  of  the  mural  quadrant. 

The  clock-corrections,  as  derived  from  the  transits  of  the  sun,  are: — 


Date. 

©•s  Dec. 

Corr. 

Clock-time  of 

Transit  over 

True  Meridian. 

Mean  Time  of 
Transit. 

Clock-correc- 
tion. 

Hourly 
Rate. 

1 701. 

• 

1 

Am        s 

h     m       s 

m       s 

J 

Sept.  19 

+   1.6 

-  7-5 

0      6       43 

23     53    40.2 

—  12    24.1 

0.72 

20 

+    1.2 

-  7-8 

5     26.2 

53     19.4 

-  12      fi.S 

21 

+  0.8 

-  8.1 

4     50.9 

52     58.6 

-   II     52.3 

0  66 

23 

+  0.1 

-  8.7. 

3     38.3 

52     '7-5 

—    II       20.8 

0.62 

24 

-  0.3 

-  8.9 

3       3« 

51     57-1 

—   II      6.0 

Interpolating  to  the  time  of  occultation,  we  have : — 

Immersion. 

Clock-correction  for  time  of  phase       —  ii"  24'. 7 


Paris  mean  time,  Sept.  22 
Greenwich  mean  time 


17"  59" 
if  50" 


25"-3 
4'.3 


Emersion. 
—  11"    24'.2 
18"  45"'  43».8 
18"    36™    22».8. 


1706,  ®  Eclipsis,  12  Mali,  mane, 
luitium  circa  8''  25"  o"  nam  hora  8  25  10  jam  apparebat  Eclipsis  quani  proximo  }i  digit 
quod  ad  visum  pertubum  patebatur. 

Postea  nubes  frequentissimae  nullas  observationes  habere  permisferunt  usque  ad  horam  8''  48'. 
Observationes  sequentes  habitae  sunt  horologio  ut  se  habet  et  non  correcto. 


May 


8'>48'   0" 

,9' 59" 

9  54  45 

II  24 

52     0 

«7  49 

56  10 

12     2 

55     ° 

'6  33 

57  45 

12  45 

57  35 

»5  17 

59  30 

13  23 

9    0  20 

■4     I 

0  50 

14     0 

I  10 

II   24 

2  25 

14  39 

7  »5 

10  46 

3  45 

IS  17 

8  40 

10     8 

5  15 

IS  55 

9  55 

9  30 

6  45 

16  33 

Transits  of©. 

4 

II  59  37 

I  49 

12     0  43 

S 

— 

I  3Si 

0  29J 

6 

59  1° 

I  23 

0  16^ 

7 

— 

I  10 

0     3i 

8 

58  46 

0  59 

59  S2.i 

9 

5836 

0  48i 

59  42i 

lO 

58  23 

0  36 

59  29i 

142 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


9"  11' 10" 

8' 

52" 

8 

25 

17  II 

Mii.v  II      II 

58    10 

0  »4         12  59  17 

12    40 

8 

'4 

9 

45 

«7  48 

12 

— 

0  13               59     6 

14    10 

7 

36 

II 

20 

18  26 

'4 

57  43 

59  56              58  494 

'5  32 

6 

58 

12 

5° 

'9     5 

17  10 

6 

20 

14 

0 

«9  43 

'8  33 

5 

42 

14 

55 

20  21 

6  Mail  pro  meridie  deterniinaudo  altitudiii 

20  25 

5 

4 

16 

10 

20  59 

22    s 

4 

26 

17 

55 

21  37 

:'  ■''                 h 

/    II 

0      / 

24   s 

3 

48 

«9 

8 

22  15 

:'■■  7 

37  36 

28  30               23  44 

26     5 

3 

10 

20 

5° 

22  S3 

40  41 

29     0               20  38 

3«     0 

2 

45 

22 

'5 

23  3' 

43  42 

29  30              »7  36 

34  IS 

3 

10 

25 

15 

24  47 

46  49 

30    0              14  30 

36  JS 

3 

48 

26 

25 

25  30 

49  54 

3°  3°              II  27 

38  26 

4 

26 

27 

52 

26     8 

52  S8i 

31     0           4     8  20 

40    0 

5 

4 

59 

10 

26  46 

41  38 

S 

42 

30 

20 

27   24 

Centrum 

0  tr.  iud.  horol.    12    0    26. 

43     0 

6 

20 

31 

32 

28     2 

44  40 

6 

58 

33 

5 

28  40 

46  20 

7 

36 

34 

36 

29  18 

47  3° 

8 

14 

36 

5 

29  56 

49     S 

8 

52 

37 

40 

30  34 

50  25 

9 

30 

40 

24 

flnis  oclipsis  accurate. 

• 

52     0 

10 

8 

53  30 

10 

46 

Tempore  eclipsis  tardabat  horologium  42". 
The  results  for  clock-error,  as  derived  from  the  transits  of  the  sun,  are  as  follows:- 


Date. 

Clock-time  of 
Transit. 

Mean  Time  of 
Transit. 

Clock-cor- 
rection. 

1706. 

Am         s 

A      m       s 

m       t 

May  10 

23     59     39.0 

23     55     59-5 

-   3     39-5 

II 

59     26.3 

55     56.8 

-  3     30.0 

12 

59     16.2 

55     54.7 

-  3     21.5 

J4 

59      0.4 

55     52.1 

-  3       8.3 

The  resulting  clock-correction  at  the  beginning  of  the  eclipse  is  —3""  22'.7,  and 
at  the  end — 3"'  21 '.9. 


0  trau.     I 
II 

Ceut. 
pro  merid. 


@  traus.    I 

Cent. 
pro  merid. 


1708,  23  Februarii. 
II  59    8 


12 


I  21 


5  Eclipsis  a  ([  Initinm  7    3  47 


12    o  14J 

12      O      I 

Feb.  24. 

11  59     2 

12  I  13 

12     o     7j 
n  59  54 


Veri  Temper  is 

7    3  48 

Finis 

7     3  57 

7     3  58 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  ^1 

1708,  Sept.  14.  inn  110.     Kclip.siH  0. 

In  niediii  eclipnis  lioiolojjiuin  tanlalmt  ex  tempore  vero  35"  He»l  eorieeto  posteii  tempore  per 
novas  obNei'vationeH  tardaliat  37". 

Ill  sequeiitibiiH  plnmihim  teiiipiiH  vernin  iiotatum  est.  Sed  ad<leii<1iiin  praeteiea  2"  propter 
novas  correctiones  quadraiitis.    Jiiitiiim  iioii  t'uit  oltNervandmn  propter  uubes. 


Diameter 

Horn  vera. 

rtiHiiliiii  .SoIIm 

Diniiititri 

illiiiiiinntn. 

6  S3  44 

29'  46" 

7  24  32 

20'  16" 

55  43 

29      8      ' 

27  31 

'9    38 

57  37 

28    30 

31   52 

19     0 

59  36 

27    52 

37  39 

18    22 

7     I  II 

27     14 

52  44 

19     0 

2  $6 

26    36 

58     I 

'9    38 

4  47 

25    58 

8     I     S 

20    16 

63s 

25    20 

20  IS 

25    20 

8  ^5 

24    42 

24  «5 

26    36 

10  14 

24      4 

25  55 

27     H 

12  13 

23    26 

27  41 

27    52 

14  20 

22     48 

30     I 

28    30 

•6  35 

22      10 

3«   55 

29      8 

18  42 

21      32 

34   1° 

29    46 

21  49 

20    54 

fi 

35  46 
n     38  40 

30    24 

Otnnea  istae  observatioues  ope  micrometri  habitae  fuerunt. 

1708. 

Sun's  Transits. 

I 

H 

C 

Sept,  10 

11"  59'  59" 

2' 

7" 

»'     3" 

II 

59    32 

I 

41 

0    3^ 

12 

59      8 

I 

'^i 

0    12J 

14 

58    20J 

0 

29 

59    24? 

IS 

57    58 

'  ,  '       ° 

6 

59      2 

16 

57    34 

59 

42 

58    38 

• 

Sept.  1 6  alt 

sup.  limb,  pro  horol. 

7  28 

55 

170  0' 

27 

17     nubes 

32 

7 

17  SO 

24 

II 

II  58  29J 

35 

i8 

18     0 

21 

2 

58  30" 

38 

30 

18  30 

4   17 

5°     (41") 

II   58  3°} 

Ergo  centrum  ©  fuit  in  meridiano  indicante  horologio  ii'>  58'  30".  Ergo,  subt.  sunt  8"  in  ait. 
0  44".  ■ 

Onines  ipsae  observatioues  ope  micrometri  iiabitae  fuerunt. 

Diameter  0  post  varias  et  repetitas  observatioues  per  transitum  per  meridianum  et  mierome- 
trum  lion  excessit  31'  48". 

Hora  7''  31'  52"  linea  ducta  per  cornua  eclipsis  distabat  a  limbo  ©  iilustrato  25'  30"  et  baec 
liiiea  ad  sensuui  horizonti  erat  equidistans. 

The  clock- corrections  are  deduced  as  follows  :  — 

Clock-times  of  sun's  transit  over  quadrant  o' 

Clock-times  of  sun's  true  meridian  .     .     .  o' 

Mean  time 23'' 

Clock-correction 


708,  Sept.  12. 

1 708,  Sept.  14. 

0'"  I  2  ".2 

23"  59"'  24».8 

0'"     6".  6 

23"  59"'  i8».6 

55""  59^9 

23"  55">  lS^4 

-4'"    6'.7 

—  4"'      0".2 

'44 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Tlu'  coiTortinii  on  moan  tinio  is  tlioroforo  — 4'"  i*  (luring  tlio  crlipso;  and  as  La 
MiKi:  liiis  alrojuly  a|)|)lio(l -|- 35'i  tlio  total  coiToction  to  liis  timos  Is  —  4"'- ^6".  Tlie 
(Mjuation  (»f  tlin(3  in  —4'"  38",  whicli  agroos  exactly  with  L\  lIiKu'a  direction  to  udd  2' 
ni<»ii3  for  rodnt'tion  to  apimront  time. 

Till- ohHcrvntioiiM  of  tlio  uclipHe  of  17 10,  28tli  Fob.,  are  given  only  In  digits  and  frnctious, 
and  tliese  only  afti-r  tliH  middle, 

17U.    Transits  of  O's  Centre. 


July 

9 

12     0 

40J 

July  16 

12     0 

S2i 

(a 

0 

47 

«7 

0 

S3i 

»♦ 

S°4 

'9 

0 

S2i 

July  IS,  Vesper,  0 

Eclipsis. 

Iluroli 

(?•» 

Portio  Ilium.  KoaiJun  Diiira. 

^h       jgtU 

0" 

30'    0" 

7"  37"'    9" 

19'    8" 

21 

0 

»7  »S 

38    23 

18  30 

24 

45 

25  30 

39    37 

17   52 

28 

30 

23  36 

40    51 

17   14 

3» 

0 

12  18 

42    S 

>6  34 

32 

«4 

21  40 

43    18 

'5  57 

33 

29 

21     2 

44    32 

15  '8 

■     34 

42 

20  24 

45    46 

14  40 

35 

SS 

19  46 

47      0 

14     2 

Tliese  cannot  be  actual  observations;  the  times  and  measures  progress  too  uniformly.* 

"Journal  des  observations  de  M.  De  La  Hire  an  mois  do  Decembre  1714. 

"L'erreur  de  sou  Quad,  etant  sur  la  flu  de  l'ann»5e  de  1 5"  soustraire  I'on  aura  les  midis  vrais 

comrae  il  suit." 

17 14.  Dec.  10  II  58  13      I  Tbe  obs.  transits  were    11  58  28 

18  II  58    li    I  "3  58  i6>^ 

1715.  MaiJ  3.  mane. 

Les  observations  de  I'eclipse,  tolles  qu'olles  font  icy  out  este  faites  avec  une  horloge  qui 
tardoit  a  I'egard  de  celle  du  cabinet  de  21". 

Eclipsis  ©  cum  novo  niicrometro. 

Digit. 


8" 


12" 

16 

'7 

25 

22 

5" 

27 

54 

32 

25 

36 

20 

41 

36 

44 

3 

46 

45 

49 

16 

52 

6 

54 

56 

57 

30 

Initium. 


0' 

0' 

I 

0 

2 

0 

3 

0 

4 

0 

4 

3° 

5 

30 

6 

0 

6 

30 

7 

0 

7 

3° 

8 

0 

8 

30 

Residuiiin. 

9''   26" 

■  0' 

29 

0 

35 
38 

31 

42 

42 

24 

44 

46 

48 

10 

5° 

50 

54 

0 

56 

51 

59 

22 

0      2 

10 

8 

32 

Digit 

10' 

30" 

10 

0 

9 
8 

0 
30 

8 

0 

7 

30 

7 

0 

6 

30 

6 

0 

5 

30 

5 

0 

4 

30 

3 

30 

"  I  am  inclined  lo  think  that  the  practice  of  "cooking  "  ohscrvalions  was  nuich  more  extensively  practiced  during  the  last 
century  'iian  is  generally  supposed.  jKAURAr  must  have  been  a  great  sinner  in  this  respect.  In  the  Memoirs  of  the  French 
Academy  for  1 779,  he  has  a  series  of  ol)servations  of  the  Pleiades,  which  are  sometimes  considered  authoritative,  but  which  a 
very  little  examination  shows  to  lie  falirications  of  the  clumsiest  sort,  so  clumsy  in  fact  that  the  author  might  be  acquitted  of 
intentional  wrong-doing  on  that  very  ground.  This  is  followed  by  a  si'ries  of  meridian  observations  of  Jupiter,  including 
//lirfiYii  cmisfcidiTf  transits,  which  give  a  uniform  motion  to  the  geocentric  position.  Among  the  observers  discussed  in  the 
present  section  I  find  none  but  I.A  Hire  guilty  of  the  objectionable  practice,  and  he  only  in  two  or  three  instances,  of  which 
the  worst  occurs  in  connection  with  the  solar  eclipse  of  1 715' 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


H5 


• 

I)i)i 

it. 

Kc'hIiImiiiii. 

.9''   0'"    4" 

9' 

0" 

10''   li" 

14" 

3'     0" 

3 

38 

9 

3° 

'4 

3-' 

2     30 

6 

3» 

10 

0 

>7 

9 

2       0 

9 

40 

10 

"5° 

22 

28 

I       0 

'S 

20 

II 

3 

»s 

33 

0    30 

22 

0 

1 1 

10  iimx. 

28 

47 

tin. 

Alia  ubNiTvittU)  0 

[w  liniigii 

ii8  0  u  lllio. 

In  Tjtbuluin  (li\  i.siiii 

1  HXHJ 

>ta 

poHt  TulfscDitiuin 

Iiiitiiini. 

8 

12 

16 

0 

9 

2S 

26 

lOJ 

'7 

I 

29 

7 

10 

20 

tj 

• 

32 

»5 

94 

22 

3 

35 

16 

9 

'5 

»i 

3« 

40 

«4 

27 

3 

4> 

47 

8 

. 

3° 

3i 

44 

30 

74 

33 

4 

47 

48 

7 

36 

44 

5° 

52 

6i 

38 

S 

53 

4° 

6 

41* 

Si 

Sf' 

43 

s4 

44 

I  "* 

0 

10 

0 

3 

5 

49 

3 

7 

2 

5° 

44 

52 

23 

74 

6 

0 

4 

SS 

30 

8 

8 

52 

34 

9 

7 

6 

10 

12 

I 

3 

9 

54 

.04 

17 

28 

t 

14 

27 

II 

32 

30 

I 

18 

S3 

II 

28 

45  Iini8. 

Diiuneter  ©  ope  niicronietri  31'  45". t  Toniporc  observationis  b()i'iil<i(;iuiu  iniisei  iuiwliTiiliat 
Hupra  vcniin  teinpii.s  16".     Igitnr  anfcreiuluin  16"  obHt-rvatioiiibus  lidnilojjii  MiisacJ. 

II  f'liut  ajontcr  5"  lY  toutcs  U'h  obscivatioii.s  c.v  ilcssus  pour  Ion  re.liiiro  au  ti'inps  vray. 

Tlii.s  18  tolliiwiHt  by  a  tliird  table,  lH>;;iiiniiiK  ^vitli  liiitiiiin  8  12  16,  and  ciidinu:  with  liiil.s  10  28 
47,  bnt,  without  any  explanation  wbatevcr  cxci'pt  "Oliservalioiici  liinitatac  ex  niei.s  .sod  cum  5"  pro 
defectn  lioroloffii".  Tlio  times  of  tliodi|{it.s  are,  lio\vever,evidently  smoothed  ott,  on  the  curve  prin- 
ciple, for  they  could  never  have  been  observed  so  nicely.     I  therefore  regard  them  as  wortlile.s.s. 

The  fourth  and  flfth  tables  are  as  follows  : — 


Inilinm. 

8   12   27 

52 

45 

74 

48  2. 

7 

'7   39 

I 

55 

41 

8 

SI   21 

rM 

20   IS 

'4 

9    « 

0 

10 

54   II 

6 

22  SI 

2 

1 1 

'5 

lOj 

56  56 

54 

25  27 

24 

14 

38 

1 1 

59  46 

5 

28    7 

3 

19 

4 

1 1 

10     2  48 

44 

3°  45 

34 

25 

37 

loi 

6     0 

4 

33  24 

4 

29 

I 

10 

9    10 

34 

36    S 

44 

32 

23 

94 

13     10 

3 

38  46 

5 

35 

43 

9 

17    42 

2 

41  29 

54 

3S 

59 

84 

22    46 

1 

.44  13 

6 

42 

1 1 

8 

28  s6  th\\». 

49  5' 

7 

45 

'7 

74 

■  , 

II  faut  retraiKiber  A,  toutea  ees  observations  6". 

[Aftir  writing  this,  1  tind  that  this  may  not  be  the  original  journal  of  La  Hire,  and  Hint  the 
doubtful  tables  are  not  found  in  the  original  journal.     The  latter  1  did  not  discover  till  latci.] 

*  41  or  4a  ;  not  legible. 

t  This  being  6"  less  than  the  real  semidiaineter,  the  question  arises  whether  the  error  is  in  the  sc^ilo  of  tliu  micrometer. 
10 75  Af.  2 


146 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Fifth  tabic. 


8  12  27 

•  nit'un 

. 

J?  43 

I 

20  23 

'A 

22  S3 

2 

2S   19 

2I 

28     7 

^ 

3'     0 

3i 

33  38 

4 

36  28 

4i 

38  46 

S 

4t  25 

S4 

44  23 

6 

•    49   14 

7 

No  ex[ilimatioii  whatever 

Mh,v  I 

12 

c  43 

2 

1 J 

0  23i 

3 

12 

0     5? 

4 

II 

59  48 

9 

II 

58  26. 

52  34 

ii 

55  41 

8 

7   17 

10 

>o     5 

loi 

«4  38 

II 

19     4 

II 

25  37 

loj 

29  18 

10 

32  26 

9i 

35  27 

9 

38  SI 

8i 

41  58 

8 

44  41 

7J 

■47   59 

7 

5»     3 

6.i 

S3  5' 

6 

56  S4 

s4 

0  14 

s 

3     « 

4* 

6   II 

4 

9     3 

3i 

J2     12 

3 

17  39 

2 

22  41 

I 

28  56  finis. 

iSmw'8  'Irandts,  etc. 


May  9. 

7  17     6 
20    9 


Sup.  limb. 
Alt.  ©  pro  borolog.  mane. 

26      O    I        40   33       II    58   36 

26  30  I  4  37  29  i  11  58  35J 


Miiy  3    Tr.  cent.  pro.  Merid.  veri  temporis   12     o     14. 

Correctiou  27"  nuferenda  a  tempore  seratino.  Addenda  igitur  10"  tempori  tranbitus  centri 
O  prociuadiHutem  muralem  in  altiludinem  centro  q  58  26. 

The  difficulty  respecting  the  duplicate  records  is  cleared  up  by  a  compari- 
son with  La  Hire's  observations  as  printed  in  the  ^' 3Icmoires"  of  the  Academy  for 
1 715.  The  first  two  tables  are  the  records  of  the  original  observations  themselves, 
which  have  been  entirely  suppressed  in  pubiication.  The  fourth  table  gives  the 
"cooked"  results  of  the  second  set  of  observatio-is  "par  I'image  du  soleil",  as  printed 
in  the  Memoirs,  and  there  is  little  doubt  that  the  third  set,  « Inch  I  did  not  cojjy,  is  the 
same  as  the  first  published  set  "avec  le  micrometre".  The  origin  of  the  fifth  table 
does  not  seem  worth  investigating. 

The  results  for  clock-error  are  as  follows : — 


Date. 

Cluck-time  of 
0's  Transit. 

A      III        s 

Mflan  Time. 

Clock-cor- 
rection. 

1715. 

A 

III           s 

1 
III      t     1 

May     I 

0      0    48.9 

23 

5f)     51-9 

-   3     bl-o 

2 

0      0     2g.8 

56     4t-0 

-   3     45.8  . 

3 

0      0     12.5 

56     36-7 

-    3     35-8 

4 

23     59     55.1 

56     30.0 

-    3     25." 

The  error  of  the  clock  witli  which  the  transits  of  the  sun  were  observed  may  be 
supposed  — 3"  37'  during  the  eclipse.  This  clock,  however,  was  not  that  with  which 
the  eclipse  was  observed:  respecting  the  latter,  we  have  only  the  statement  that  itwps 
21  seconds  slower.     The  correction  of  the  clock  actually  used  was  therefore 

—  3"'  i6*. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


147 


1715,  25  July.     Mane.    Oticiilt.  y  a  S 
ImincrHio  liinlti  ])riuri.s  U  in  paiteni  luiiiie  liicidain     .     . 

liiiihi  p().stui'ioi'i.s  U 

Liinl)u»  prioris  U  et  tniii.sit  iiiinierHioni.s 

linsterioris 

July  22.  ©  centre  transit n  S9  584 

23-  59  40.^ 

((  IhnU.  poat 6  20  16 

Veri  tempore,  (Jna.  mur.      .  6  20  34 

per  merit].      .  6 


'  3'  35 

1  32  51 

2  17  21 
2  18  37 


24. 


U  tr.  centri 7 

true  time 

per  meridian 


20  38 

8   loj 
29 

39 


[i.  e.,  he  adds  18"  for  clockcor- 
rt'ction  and  4"  for  error  of 
quadrant.] 


[So  be  considers    the  correc- 
tion 10".] 


©  tr.  centri     .    .    .    .    .    .    n  59  25J 

per  meridian >'  59  3li    [Correction  12",  it  seems.] 

July  25.  0  centre  tr •'  59    7J  • 

per  meridian 11  59  rg 

I  find  no  further  data  for  the  correction  of  the  quadrant. 

From  the  transits  of  the  sun  v.'e  have : — 


Date. 

G's  Dec. 

Corr. 

Clock-time  of 

Transit  over 

True  Meridian. 

Mean  Time  of 
Transit. 

Clock-cor- 
rection. 

m        s 
H-   5     36-0 
+  5     56-3 
+  6     14- 2 
+  6     33-9 

Hourly 
Rate. 

July  22 
23 
24 

25 

+  20.3 
20. 1 
ly.g 
10.7 

+    13-4 
131 
12.8 
12.5 

/t      in        s 
0      0     1 1 .  () 
II     59     53.8 
II     59     38.0 
II      59     19-7 

/i    in        s 
0     5     17-9 
0     5     50.1 
0     5     52.2 
0     5     53-6 

s 
0.84 

0.75 
0.S2 

(3) 

(4) 

-f6"'   2  5».S 

+6     25".8 

"  23"  46^.8 

2''   25'"     2^8 

"   14'"  2  5".S 

2"  15"'  41".; 

Interpolating  between  the  transits  of  the  sun  on  July  24  and  25,  we  find,  for  the 
times  of  the  four  contacts : — 

(9) 

-r6"'  2  5-.3 
i"  39""   1 6^3 
i"  29'"  55"-3 
1718,  Sept.  9. 
8  43  34     I'linmerNion  d'une  petite  etoile  par  le  corps  de  la  lune. 
Sept.  5  0  tr.  II  58  57.J  12     I     7  •   12     o     2J 

8  57  32I  59  40A  58  36J 

>o  5(>  3Si  58  43*  57  39i 

The  dock-corrections  from  the  transits  of  the  sun  are : — 


(I) 
Clock-corrections  +6'"  2  5".3 

Paris  mean  times  i''  38'"     o".3 

Greenwich  mean  times    i*"  28'"  39".3 


Dale. 

©■s  Dec. 

Coir. 

1718. 

0 

s 

Sept.    5 

+  6.8 

-  3-3 

8 

5-7 

4.2     j 

10 

4.9 

4-" 

Clock-lline  01 

Transii  over 

True  Meridian. 


A      m  .<■ 

12     5.)  58..) 

58  32.3 

57  34  f- 


Mean  Time  of 
Transii. 

C'lock-cor- 
rection. 

m       s 

-  I     28.7 

-  .       ..5 

-  0    44,4 

ilonrly 
Rate. 

//      m         s 
23     58     30.2 
57     30.8 
5O     50.2 

s 

0.38 
0.36 

148 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


-   49'-9 

8"  42™  44».i 
8"  33'''  23'. I. 


We  honce  obtain  : — 

Clock-correction  foi*  the  time  of  immei'sion     .     .     . 

Paris  mean  time,  September  9       

Greenwich  mean  time 

The  star  is  li.  A.  C.  8184. 

Series  III. 

Observations  by  Delisle  at  or  near  the  Luxemburg. 

Volume  113,  MS.  No.  1012.    Observations  Astrononiiquea,  fnit«s  au  Luxembourg  par  De  I'Isle. 
(About  750  toises  north  of  the  Observatory.) 


1 7 13,  Noveiiibre  30.     0  011  gnomon 
Dec.  I.     "   "        " 


OecnItatioM  ol'  r  Tauri  (stli  mag.),  2  Dec,  matin 
Dec. 

4- 


3.     0  on  gnomon 


n  59  Sl'i 
o     o  24J 

o    9  19  clock;     o  ?8  39^  t.  vr. 
o     I   22J 

o     I  54 


1713,  June  21.    Error  of  gnomon  per  e<(nal  tiltitudes  less  than  i". 

17 14,  .Tan.  26.    ]\Iorning  alt.  8''  49"'  o"  =  evening  alt.  3''  12'"  47'. 

]\[ean  of  this  autl  8  others  gives  transit  of  0  = 

(The  correction  tor  change  of  dec.  being  —13'.) 
0  on  gnomon 


o  o  41.2 


From  the  ol)servations  on  January  26,  17 14,  the  correction  of  the  gnomon  is 
abont  +o".4.  This  correction  may  be  considered  as  applicable  to  the  transits  of 
December  1  and  3  previons.    AVe  thns  have: — 

1713,  Dec.  I. 

Clock-times  of  0's  transit    ....  o''  o™  24".9 

Mean  times .  —10™  2  7».o 

Clock-corrections        — 10'"  5i".9 

Clock-time  of  occnltation  of  r  Tauri,  Dec.  i      .     .     .     . 

Clock-correction 

Paris  mean  tmie Ii''  58"'   24^.3 

Greenwich  mean  time 11''  49'"     3''.3. 

1714,  Mar  20.     Imm.  of  *  U  of  6th  mag    ...       9     6  50     clock.       9     8  21   t.  vr. 

The  star  passcil  only  4'  within  tht  moon's  southern  limb. 
1714,  Marai.     Iinin.  of  »  Tauri,  6th  mag.       .     .      lo  15  54^  clock.     10  18     9^  t.  v, 

Cette  immersion  a  Hi'.  ol)servee  ,i  I'observaloire  a  lo  i8  9  t.  vray. 

Mar  17.     0  on  meridian  per  equal  altiintles  (6  ill  number)   .    .      o    045^* 

"      "    "  gnomon , 

18.     "    "        "  

11    (.        11 


1713,  Dec.  3. 

Qh     jm 

23".  2 

-   9" 

39"-9 

—  n'" 

3M. 

1 2''     9'" 

19'. 

—  lO™ 

54"- 7 

20. 

"     "    "    mei'idian  per  10  equal  altituden 
21.     ''  Limb  on  gnomon         


Transit  of  semidiameter  from  other  davs 


o     o  44i  < 
004^ 

'I   58  45 
>i  58  45-4 
II   59     8 

'     5 


"  Le  pendule  a  retardi  de  23"  dn  le  20  au  21  snr  le  moien  monve.     ?i  58    3 
du  Soleil." 

22.     0  011  gnomon "57  21J 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


149 


Applying  +o'.7  for  correction  of  gnomon,  we  have  the  following  clock-correc- 
tions from  transits  of  the  snn : — 


Date. 

Clock-time  of 
Transit  of 

0  over  True 
Meridian. 

"Mean  Time  of 
Transit. 

Clocli-cor-  ! 
reclion. 

1714- 
Mar.  17 

h      m        s 
0      0     45.2 

h     m         s 
0     3     41.2 

m        s 
+  7     56.0  ^ 

18 

0      0       5.2 

0     8     23.4 

+  8     18.2 

20 

II     58     45 -^ 

0     7     46 . 8 

+  9       1-4 

21 

II     5S       3-7 

0     7     28.4 

+  q    24-7 

22 

II     57     22.2 

0     7       9.8 

+  9    47-<>  j 

The  clock-rate  seems  very  good  for  this  epoch.  Interpolating  the  clock-correc- 
tions to  the  times  of  the  occultations,  we  have : — 

1714,  Mar.  20,  )|c  B.  1714,  Mar.  21,  oTanri. 

Clock-times  of  occultation        .     .  9''     6"'  50".  10''   15™  54».5 

Clock-corrections        -fg™  io'-2  +9"'  34-''4 

Paris  mean  times         9''   16"'     o».2  10''  25'"  28».9 

Greenwich  mean  times    ....  9''     6""  39^.2  10''  16'"  f.C). 

I  have  not  certainly  identified  *  B,  but  it  is  near  B.  A.  C.  1373. 

1714,  April  7,  Miitin.     Imin.  of  I  Sagittiirii  (l)ii},'lit  liinli).  .     •     .    32048    dock.    3  24  22.J  t.  vr. 
(SiuUlenly  to  the  JsL'coud),  Einer.sion  (ihiik  liiiih).       1    u     i.^  clock.    4  37  3''^     f- vr 

II  y  avoit  (leja  qnelques  sei'oiuls  (jik  I'i'tolle  avoit  toiicli(/  le  boul  eclaire  tie  la  luiio  &  elle 
paniLssoit  se  ineler  avec  I'oiidiilatioii  (iiii  w        -nit  tout  autoiir  dii  bonl  eciaiie. 

(Page  75.)  He  adds  that  at  tbe  Oliservato,  'lit'  .ili.seivcd  t  iiiics  were,  Iiiimeision  :;  19;  Eiiier- 
sioii  4  37  25.  He  is  surpiitied  at  the  ditl'ereiiees  ol  3' j  and  1  -,%  and  enters  into  a  Imm  an onnt  of  his 
grounds  for  believing  that  the  error  is  not  on  his  snh-  lie  only  weak  point  beinj;  the  want  of  a 
clock  error  between  the  5th  and  8th.  He  eonsiilers  it  possible,  however,  tluf  In-  may  have  forgotten 
to  subtract  the  io»  which  he  counted  between  tlie  moment  of  eiiiersion  and  tn  it  of  noting  the  clock- 
time;  if  80,  his  time  should  be  4  37  28. 

Apr.    5.     0  on  gnomon,  11  57  32! 

8.  "   "         "         II  55  30 

9.  "   "         "         II  54  5° 
10.     "   "  "         II  54    6 

Applying -fo". 5  for  gnomon,  we  have: — 

1714,  April  5.  17'       '  iiril  8. 

Clock-times  of  O'rt  transit   .     .     1 1"  57'"  SS'o  • ''  ..V"  3o''-5 

Mean  times o"    2'"  48".;  o"     i"'  55».6 

Clock-corrections +5'"' 5"- 7  4-6'"  ?  5"  i. 

Occultation  of  ^  Sagittarii,  April  6 : —  ' 

IniniLTHion.  Emersion. 

Clock-times  of  observation      .  15"  20'"  4.S'  16"  34"'     I'.s 

Clock-corrections +  5'"  53"-6  +  5'"  54"-8 

Paris  mean  times 15"  26'"  4r.6  16"  39™  5 6". 3 

Greenwich  mean  times  .     .     .  15''  17"  2o".6  ±  2»  iG"- 30    35".3  ±  2'. 


I50 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


These  times  agree  so  well  with  those  noted  at  the  Observatory  (see  jiost)  that 
his  opinion  t>f  o  difFerence  of  ten  seconds  seems  to  be  erroneous. 


La  peudule  a  6t6  avancde  ile  2  minutes. 
La  pend.  a  6t6  avanc<Se  i  minute. 

Pend.  avanced  i  minute. 


1714,  Sept.  27  (p.  101),  Soir  Emeisioii  of  Tuuri  (stli  mag.),  darli  limb,        9  18  42   cl.    9  19  8J  t.  vr. 
Oct.      3.  Miitiii  Em.  oi  «  (?)  Scoipii,  very  exact,  daik  limb,  2  58  14   cl.     2  58  9    t.  vr. 

Sept.   19.     0  on  gnoinoii    .     .     .     11  58     7 

20 II  59  46^ 

22.    Second  limb      ...      o    o  19 

-  I     3-J 

24.  Second  limb      ...      o    o  38 

-  I     3i 

25.  Cent 'I  59  i6i 

26 II  59  584 

27 II  59  4oA(?)  Le  fll  n'etoit  pas  trop  bien  place  anprfes 

(In  pied  du  style. 
Oct.      I II  58  31         La  pend.  avaiic(5e  2  minutes. 

2-  O       O    I4J 

3 II   59  59 J  \ 

5 II  59  3oi 

It  cannot  be  inlerred  from  the  statements  whether  the  clock  was  put  forward  before  or  after 
the  transits  of  the  sun. 

Applying  no  correction  to  the  gnomon,  which  seems  to  have  been  adjusted  with 
great  care,  we  have  the  following  results  for  clock-correction : — 


Date. 

Clock-time  of 
©'s    "ransit. 

M 

.•an  Time. 

Clock-cor- 
rection. 

1714. 

Am         s 

A 

m 

s 

m       s 

Sept.  26 

11     59     58.5 

51 

ig.g 

-  8     38.6 

Sept.  27 

II     5(J     -10.5 

51 

0.0 

-  8    40.5 

Oct.     1 

u     53     31.0 

49 

42.4 

-  8     48.6 

Oct.    2 

0      0     14  5 

■19 

23.8 

-10     50.7 

Oct.    3 

II     59     59-5 

49 

5-4 

-10     54.1 

We  hence  deduce : — 

'•-  Taiiri.  (I  ("aiicri. 

Clock-times  of  emersion,  1714,  Sejjt.  27,  9''  18'"  42'.  Oct.  2,  14''  58""  14'. 

Clock-corrections — 8"' 41 '.3.  —  10™  5  2"  7. 

Paris  mean  times g*"  10'"    o'.7.  14'' 47'"  21 '.3. 

Greenwich  mean  times g*"    o"' 39".7.  14'' 38""    o".3. 

The  designation  of  the  second  .star  is  clearly  a  mi.stake. 

1715,  May  3,  Matin.     Beginning  of  Eclip.se  0    .    .     8  12  57  rlock=r8  12  35  t.  vr. 

End ,     8  28     o  =8  28  38 

IJnt  owing  to  the  intervention  of  cloud.s,  lie  is  not  siiro  but  that  the  latter  moment  is  some 
seconds  too  early. 

La  pendulo  a  it6  arrets. 

Centre. 

May    I.    ©  L  limb  on  gnomon      n  58  4si -h  i     6 

2.    Centre       n  59  35 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  1 5 1 

June  28.  He  does  not  give  th6  clock-times  of  tlie  occultatiou  of  Venus,  but  only  the  t.  vr. 
I  30  19  and  2  37  17,  as  already  printed. 

"Ju  suis  sorti  de  Luxembourg  :t  la  fin  dn  niois  de  Suptembre  1715  par  urdre  de  Madame  la 
Duchesse  de  Berry," 

The  observations  of  the  eclipse  on  May  2  do  not  admit  of  an  accurate  reduction, 
owing  to  the  stopjiing  of  the  clock.     Uelisle's  reduction  may  therefore  be  accepted. 
The  equation  of  time  being  —  3"'  22",  the  times  are : — 

Beginning  of  eclipse  ......     8''    9™  13"  Paris  mean  time. 

9^  59™  53'  Greenwich  mean  time. 

End  of  eclipse S*"  25"  16"  Paris  mean  time. 

The  next  observations  are  made  at  the  Hotel  de  Tairamie,  about  1'  north  of  the 
Observatory,  and  about  0".^  west,  so  that  the  longitude  east  of  Greenwich  may  be 
supposed  9'"  20'.3. 

Volume  114,  No.  1023. 
•  Page  90. — Occultation  of  Aldebaran,i7i7,  Sept.  25,  soir. 
"Le  bord  de  la  lune  etait  dentet6  li.  cause  de  sa  i)roximite  i\  I'liorlzon  &  Aldeb.  toucha  cette 
denteture  ^  9  12  15  de  la  pendule,  au  quel  tema  ,je  ne  le  pus  plus  dislinguer.     Le  teins  viai  est  A 

9  II  38." 

Emersion,  dans  uu  iiistaut  10  4  34^,  Pend.  =103  57. 

Sept.  25.  Alt.  0  Lower  L.  *  • 

Midy  vrny. 
-  73127  16°  35'  4     I     3  II  46  36    "I 

3340  16    SS  35854  38    I      Movenix46  37.2. 

3S  51  17    15  5641  37 

38    2  17    35  5431  37i  ) 

La  pendule  a  6t<5  avanc^e  de  14'. 

Sept.  26.  Alt.  ©  12  obs.    The  first  and  last  are: — 

74723  163s  4  13    8  o.  36i» 

o  ,„  ,,  .Q  1  I   Mean  of  12,  o  o  38.1  ;  gnomon  002-;. 

8  II  53  2015  3  48  44  o  o  39*  >  '         ->   2  >  »  J 

The  clock-coiTections  are  derived  as  follows: — 

1717,  Sept.  25.  1717,  Sept.  26. 

Clock-times  of  O's  transit o''    o'"  37".2  o''    o'"  38".3 

Mean  times 23''  si""  34^.6  23''  51™  i4'.6' 

—  9"'    2".6  —9™  23'.;. 
Occultation  of  a  Tauri :  — 

ImninrHion.  Enicrsioii. 

Clock-times 9''  12"'  15'        10''    4'"  3 4". 5 

Clock-coiTCctions —9"'  lo".;         —9'"  ii".5 

Paris  mean  times,  Sej)tember  25     .     .     .       9''    3"'    4^.3       9''  55""  23'.o 
Greenwich  mean  times 8''  53™  44^.0       9''  46'"     2'./. 

But  the  immersion  may  be  observed  a  little  early. 

1718,  Jan.  16.  i""  27'  14".  Immersion  of  ^  Geminorum  (i5''.6,  I  think). 

Jan.  16.  Tr.  of  sun  per.  (iorresp.  altitudes  (iincorr.) 0413.8 

Mean  interval,  e""  i2"'corr.     . u. 

Gnomon  o''  4'  i".o  =  <!> o  4    2.8 

Jau.  II.    *  =  o    7    1      et  8' a  6te  retrrtneh(5. 
Jan.  12.  II  59  57  . 

16.  o    4    i.o  la  pendule  a  et6  retarde  de  4'. 

18,  O      2   29.5 


152 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Addiii}''  I'  for  gnomon,  taking  the  time  of  transit  for  Jannary  i6  from  the  corre- 
sponding altitndes  (true  correction  —  1 1".6),  and  reducing  the  artificial  changes  in  the 
clock  to  its  state  on  Jannary  15,  we  have : — 


Date. 

©'s  Transit 
per  Clock. 

Mean  Time  of 
Transit. 

Clock-cor- 
rection. 

m        s 

Hourly 
Rate. 

1718. 

h      fPi          s 

//       in        s. 

Jan.  II 
12 

II     59       2.0 
II     59     58.0 

0      8     33.3 
8     56.6 

+  9     31-3 
f     58.6 

-  i.3f' 

-  1.64 

x6 

18 

0      4       2.2 

0       6,    30.5 

10  23.7 

11  3-J 

6     21.5 
+   4     32.6 

—    2.27 

Interpolating  the  clock-correction  to  the  time  of  observation,  we  have: — 
Clock-time  of  immersion  of  A  Geminorum,  1718,  Jan.  15  .  .  .  13''  27"  14" 
Clock-correction       +6"  41" 


Paris  mean  time 


13"  33"'  55" 


Greenwich  mean  time        13''  24"  34'. 7  ±  2". 

Page  127.  —  1718,  Feb.  9.  Siiir.  Inim.  Aldebaraii •  6  19  44  =  6  16  48  t.  vr.,  or  6  16  53? 
wliitili  he  thinks  is  more  e.^at't,  hecaiLse  defived  from  trausits  of  stars  as  well  as  ©.  Afterward  he 
finds  that  6  16  48  is  after  all  tlie  most  probable  time  from  tlie  mean  of  all  methods.  The  probable 
error  does  not  seem  to  be  .so  iiuich  as  2' 

Feb.  6.  ©  on  giioinoii 0841     Pend.  ret.  9  inin. 

Clock  has  gained  5'  since  Feb.  i,  about  1'  per  day. 

Feb.  10.  ©  on  gnomon        o  3  39 

The  correction  to  gnomon  is  -|-  o'.y. 

Accepting  Dkllslk's  reduction,  the  equation  of  time  being  -f- 14"'  47*.4,  we  have: — 

Paris  mean  time  of  occnltation  of  Aldebaran,  1718,  Feb.  9       .     .     6'' 31"' 35".4 


Greenwich  mean  time 6'' 


22'"  15".!  ±  2". 


Page  133. — "Looiiis,  Feb.  14,  soir,  I'etoile  a  paru  toucher  dans  son  inniiersion  la  partieeclair<5e. 
J'ai  ces.sd  de  i'apercevoir  a  6  52  39  de  la  pendnle. 

Feb.  14.  ©  on  gnomon,  o   7  43. 

15.  08  43. 

It  seems  doubtful  whether  the  immersion  of  n  Leonis  is  worth  using.  The  real 
occnltation  was  probably  not  seen.  There  is  room  for  suspecting  a  change  in  the  cor- 
rection to  the  gnomon. 

1718.  Sept.  9. 
8''  44'  49"  Une  etoile  se  cache  sous  le  bord  de  la  lune. 
46 


,      Nov.  8. — 12  corr.  alts.  ©. 

Mean  int.      ...      6''  23'" 
Uncorr.  tuean    .     .      03     58.3 

Corr +16 

Aug.  19.  Mean  int.  11    28 
Mean  of  9  corr.  alts,     o      i    32.1 
Correction     ...  20 


8    45 

35 

Cent. 

Aug.  19. 

© 

tr. 

0"    0'  45" 

2'  56" 

,'  5o"A 

Sept.   5. 

It    58    .7.1 

0   26.J 

59    2  2 

J- 

58    i.i 

0    21 

59    «63 

8. 

58      9 

0    17 

59    «3 

10. 

58    II 

0    19 

59    >5 

Nov.    8. 

3      8t 

5    25 

4    '6J 

•This  same  occnltation  I)bi.isi.e  says  was  observed  at  Toulon,  "clans  le  Semenaire  Royal  de  la  Marine,"  by  Le  P.  Laval. 

tnim.  64027,  Lm.  74740,  iJur.  i  7  13;  the  clock  being  coriected  by  different  corresiMnding  heights  of  the  sun  on  the  9lh 

and  lolh. 

t  Somewhat  doubtful,  from  being  obliged  to  use  a  watch  in  counting  the  seconds. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


153 


T\\Q  results  for  clock-error  are  flerived  thus:  — 


Date. 

Clock-time  of 
©'s  Transit. 

Meai 

Time. 

Clock-cor- 
rection. 

Mou'ly 
Rate. 

1718. 

A      in        s 

m 

s 

m        s 

Sept.   5 

II     59     32.5 

58 

30.3 

-    0     52.2 

+    0.72  : 

7 

17-3 

57 

50.7 

1     26.6 

+    0.67  ! 

8; 

'3.5 

57 

30.8 

I     42.7 

+     o.Sq  ! 

10 

15-5 

.. 

50.2 

-  2     25.3 

1 

We  have: — 

Aug.  19.  Correction  of  etju.'il  altitudes +21'.  1 

True  transit o"  i"  53". 2 

Gnomon i'"  So'-S 

Con-ection +    2".7, 

Nov.  8.     Correction  of  equal  altitudes +1 5'.8 

I'nie  transit        4'"  i4".i 

Gnomon 4'"  i6"-5 

Correction .  —    2^.4. 

I  have  used  4-o'.5.  . 

We  then  have,  for  the  time  of  occultation  :  — 

Clock-time,  1 718,  September  9 8'' 44'"  49". 

Clock-correction —2'"  11  ".8 

Paris  mean  time 8   42'"  37'.2 

Greenwich  mean  time 8' 33"  i6'.9J::2". 

I'agH  245. — 1719.  Apr.  22,  .soil'.     Imui.  A.kleb.  dark  limb,  7  44  44  clotiiv  =  7  44  32  t.  vr. 

Em.        "       brigbt  "     8  34  24  =8  34  14 

Daub  cette  observation  I'etoile  ii'etoit  point  encore  detaclice  dti  boid  eclaire  de  la  hino. 
Apr.  22.  True  noon  per  13  pairs  equal  altitudes      o    031.7 

©  on  gnomon  o    o  3^-5 

23.    "   "        "  II  S9  3'-S 


The  results  of  the  observations  are : — 

Clock-times  of  sun's  transit o'' 


Apr. 


Mean  times 25"  58" 

Clock-corrections —  2' 


3i'-7 
?5'.8 

5"-9 


Ajir.  23 
II"  59 

23"  58 
—  I 


1"   -if->' 


13' 

'7' 


4 
■3- 


Occultation  of  Aldebaran. 


Clock-time^' of  phase,  i  719,  April  22 

Clock-coiTections • . 

Paris  mean  times 

Greenwich  mean  tinier      .... 
20 75  Ap.  2 


Iiiiiuei'siou. 

7   44    44 
—  1'"  50".  2 

53'-8 
33"-5 


7"  42" 


7"  33" 


Kiiiersioii. 

8''  34'"  24". 

—  1'"  4S».6 
8''  32™  J5'.4 
8''  23'"  1 5". I. 


154  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

I'li^o  249- — 1719,  Auj?.  21.  Iiiiin.  y  Libriis  very  exact,  7  41  31  nl.  =  7  40  12  t.  vr. 
.  E(iiuil  tiltittult's  ot  ©'«  lower  liiMl)(?). 
All''.  21. 


AH. 

11O4.' 

'3   4?, 

•4    '5 

20  J  5 

=°  45 

21  . 


A.  M. 

6  31  42A 
44  °A 
47    3 

7  24  47 
26  47 

28.4 


r.  -M. 

6    5  28J 
5  53  '3 

5°    3 

12  32 

10  32 

837 


Aiif;.  22. 
A.  M. 

0  16  43 

28  58J 
32     o 


Mean  Aug.  22.0 
Coir.       .    . 


Subtr. 


o  18  40 
+  19 

o  !8  59 
19    o 


7  "  47i       Aug.  22.0    .     .         .     .     1 1  59  59 

'352         Aug.  22.5.  Mean  of  last  2,    o    140 

Correct 23 


023 


(.!l<>('k  put  b:!ck  19  tniiiutfs  l)et\veeii  Aug.  21,  p.  111.,  aud  Aug.  22,  a.  in. 
Owiiin  111  riouds  ami  fog,  Dklisle  rejects  tlie  tliiec  top  linca  altogether. 

1)em.slk's  f  nrrection  for  midnight  seeiiLs  all  wrong.  The  corrections  for  noon  and 
niidiiight  are  4-'>*^'-6  and  — 2  7".4  respectively,  whence  we  obtain: — 

1719,  Aug.  21.0.  1719,  Aug.  21.5. 

tiock-tiincH  of  siin'.^  transit,  corrected  lor  change  of  19'"     23''  59'"  58".4      12''     i'"  I2'.2 

IVfean  times o''    2'"  51  ".2      12''    2'"44'. i 

Clock-corrections +2"'52".8  4-i"'3i'.9 

Clock-time  of  immersion  of  y  Librif,  1719,  Angnst  21       .  7'' 41'"  31". 

Clock-correction -|- 2'"     i".  i 

I'aris  mean  time 7''  43'"  32".! 

Greenwich  mean  time z""  34™  ii'-8. 

The  dates  Ang.  22.0  and  Ang.  22.5  in  my  manu.script,  and  as  printed  above  with- 
out change,  are,  without  serious  doubt,  one  day  in  error.  'I'iie  computation  is,  how- 
ever, that  f>f  Dei-isle,  ami  it  is  evident  that  he  has  deduced  his  "  Temps  vray"  from 
the  erroneous  deduction  of  the  clock-time  of  midnigiit. 

I'.ige  259.  — 1719,  Oct.  3o(?)  Iiiiinersiou  of  Altlebaran  (inst.)  8  56  34  clock  =9     2  54  t.  vr. 

Emersion,  dark  limb.     ...      9  S3    3j  =  9  39  29^ 

Duration 56  29J 

Oct.  29.     Efpial  alt.  ©.  Oct.  30.     12  altitudes  very  accordant. 

8  27  27  3  13  45  7"  47'  12"  70  25'  4''     i'  i4"i 

30     o  II      9  ...  .        .  ... 

32  38  8  32  ...  .-     ..  ... 

35  214  S  49  ...  .       .  ... 

7,^     ik  3     5  8    13    56  us  '           3     34  29 

40  46  o  24 


Mean  noon  Oct.  29 n  5°  35  Mean  of  12 

i8i        Correction 


Corrected u   5°  534 

Clock  advanced 60 


II  54  12.9 
+  '9-5 

II  54  32-S 


"  56  S3 J 


RESEARCHES  ON  THK  MOTION  OF  THE  MOON.  155 

The  coiToctioiis  for  motion  of  huh  in  ileclination  I  iimltD  Uo  +  ''*^'6  mid  +  ig'.o. 
The  rocUiction  of  the  ol)s(>rvation.s  thcrcfon'  stiMids: — 

1719,  Ocl.  29.  1719,  Oit.  30. 

Clock-timc'h  i»f  tninisit  of  O     ....      i  i""  56'"  53^.6  11''  54'"  3i".9 

Mean  times        i  1''  43""  58".o  11''  43'"   54".8 

(JU»ek-coiTeetions        .      —     12'"   55'.6  —     10'"  37".i. 

The  elock-correittion  nnist  now  he  cari'ied  forward  eight  hours  with  the  rate 
derived  from  the  observations  of  the  two  (hiyn. 

Occi(lt(itio)i  of  Alilcharnn. 

iDimoi'Hioii.  EiUHrHiou. 

Clock-times  of  phase,  1719,00^30      .     8''  56'"  34'.  9''  53'"     3".5 

Clock-correetions — 9""  44^9  —9'"  39'.4 

Paris  mean  times 8''  46"  49".  i  g*"  43"'  24".! 

Greenwich  mean  times 3"  37'"  28".8  ±3"         9"  34™     i'-S  ±3"- 

These  times  are  1"  greater  than  those  obtained  1»y  eorrecting  I)eli8i.i:'.s  result 
for  the  equation  of  time,  —16'"  6".  The  ditferenee  arises  from  tiie  change  of  o".5  in 
the  correction  for  noon  on  October  30. 

Total  I'ciipsf  <>l  ©,  1724,  May  22.8  (?).  21!  part  of  i)a},'i"  95.  At  the  Royal  Observatory, 
wliitlu-r  lie  had  transpoitcil  his  iiistruiiifiits. 

J'ay  (!OIiiiiioih:o  a  I'api'rct'voir  a  5''  53'  24"  de  ma  peiidulc,  inais  le  vray  coiniiu'iicfiiiciit  a  pen 
arrivcr  uii  pini  plustot,  parceqai'  jc  iie  ivKaiiiois  pus  dans  ue  teiiis  hi  pivcisemeiit  i\  I'mdroit  011  la 
lime  est  entree,  et  que  Je  ne  ni'eii  siiis  apeien  (|iie  lor.sriii'elle  ocenpoit  line  petite  portion  <le  qiiehpies 
denies  du  l)ord  dii  soleil.  U'  teiiis  vray  est  H  5  55  18  d'ou  je  crois  poiivoir  mettre  le  coniuieiice- 
ineiit  ii  s  55  o.  LaTotalite  m'a  para  se  tain' a  6''  46  55  pend  =  6  48  54  t.  vr.  Le  rccouvienient 
de  luniiero  in'a  aussi  jjara  se  faiiv  6  49   ij  =6  51    12,  ainsi  I'oh.scuiite  a  duie  2'  18". 

May  21.  Casslni's  clock  at  app.  noon  11  57  o  from  16  eqaal  alts.  He  afterward  put  the 
clock  forward  3'.     Allowing  lor  this,  the  sun  passed  the  mural  quadrant  as  follows:— 

May  21  II  59  56 

22  II  59  3I 

24  II  59  48 

(loinparison  of  clocks.  May  22,  evening. 
DET.tSLE  3  18  27         19  27  5     3  16^        4  164  7   "     4        12     3J 

(JASSINI  20     o  21      o  50  60  13     o  14     o 

Dili.  I  33  I  33  '  43*         "  43J  '   S<>  '   5^4 

I  have  not  yet  reduced  and  discussed  these  observations. 
1725,  Feb.  19.5.     liniu.  of  TiUiri,  exii;t  ilirk  linr>.    o"'  14'  24"  =  o''  11'  18"  t.  vr. 

Correitious  of  Gnomon.  TrRnsits  of  0  over  Gnomon. 

s 

Jan.    8  o.o  Feb.  17        o     2     44 

Sept.  13  +  ::.7  19        o     2  52.7 

20  —0-7  2°         °     3   '9-' 

Assuming  the  gnomon  to  be  correct,  the  reduction  stands: — 

Keb.   19.  Fell.  -20. 

Clock-times  of  transit o"     2"'  5 2". 7         o"     3'"    19".! 

Mean  times o"   14"'   18".  7         o''   14'"   i2".o 

Clock-corrections  + 1 1-"  26".o  +10™   52-.9. 


'56 


RESEARCHES  ON  THE  MOTION  OK  THE  MOON. 


ImtiHTsion  of  A' Tauri,  clock-tinif,  1725,  Feb.  19 

( 'lock-coiTectioii 

I'iiris  inoiiii  tiino 

Greciiwicli  moan  tiiuo 


12''   14""  24". 

+  11'"      9".2 

12''    25'"  33". 2 

12''     16'"  I2".Q. 


Serikm  IV. 

Tliis  is  porliaps  to  some  extent  a  ('(tntinuation  of  Series  I.,  by  tlie  Cashinih  and 
.M.\K.\M>is.  1  liave  not  attempted  to  identify  the  individnal  obHcrvers.  The  Hystom 
of  oltscrvation  was  the  same  as  before,  the  transits  of  the  sun  beinjr  rejjfnhirly  observed 
witli  the  niiirai  (pnub-ant,  and  the  true  times  of  transit  oec'asionally  determined  by 
corresi)ondin^  altitnth^s,  and  the  eorrection  of  tlie  qnacb'ant  thence  determined  I  have 
re-reduced  all  these  observati<ms  tliat  I  couhl  find.  There  is,  however,  a  hiatus  extend- 
in;;- from  i7J(S  to  1756,  within  which  an  entirely  independent  derivation  of  dock-errors 
does  not  .seem  |)ossible.  Tluis,  curious  tliou^h  it  may  seem,  tlie  place  of  the  moon  is 
much  better  determined  during-  the  first  (piarter  of  the  last  century  than  during'  the 
second. 

The  computation  of  the  eorrection  of  the  (juadrant  from  the  sets  of  equal  alti- 
tudes is  sliown  in  tiie  following  talde,  which  does  not  seem  to  need  any  special  ex- 
planation. 

ImwstigalioH  of  Corrections  to  tlie  Riris  Quadrant,  1706-1758. 


I);iti'. 

Clock-lime  of 

Mean  of 

(Corresponding 

Altitudes. 

Mean 
Interval. 

Hourly 
Motion  of 
Sun's  Dec. 

Corr.  for 
Motion. 

s 

('lock-time  of 

Transit  over 

Meri<lian. 

Ill             s 

Clock-time  of 

Transit  over 

Ouadrant. 

Ill            s 

Corr.  of 
yuadrant. 

J 

Sun's 
clinat 

0 

De- : 

ion.  • 

/;       ;// 

// 

m 

/ 

1706,  May   14 

23      5C)      20.2 

4 

14 

+   36-4 

- 

S.I 

59 

12. 1 

59 

42. 0 

-   29.9 

4-18 

35  i 

AllR.     I 

23     55      15-4 

6 

13 

-  37.6 

+ 

9-9 

55 

25.3 

55 

590 

-  33-7 

+  18 

6  • 

Sept.  Iij 

23     58     4O.0 

4 

54 

-   58.2 

+ 

"7-9 

59 

3-9 

59 

390 

-  35-1 

+    I 

34 

Dec.    5 

23     58     52-2 

4 

3i 

—    iy.2 

+ 

7-7 

58 

59-9 

• 

—  22 

22   . 

1707,  April  4 

23      50      2().2 

4 

25 

+    57.3 

- 

If..  5 

50 

9-7 

50 

47-5 

-  37.8 

+   5 

32 

Jiinc  K) 

23     55     32.2 

5 

35 

+      2.S 

- 

0.6 

55 

31.6 

56 

2.0 

-   .30-4 

-H23 

26 

Sept.    6 

23     58       S.7 

4 

42 

-    55-8 

+ 

15.8 

58 

24-5 

59 

o.S 

-   36.3 

+   6 

37  1 

1708,  Pel).  24 

23     56     25.5 

4 

'3 

+  44.4 

- 

10. 6 

5f> 

8.g 

56 

44.0 

-  35.1 

-16 

25  1 

July     >) 

23     58     31.9 

4 

33 

-    18.2 

+ 

4.3 

58 

3f).2 

59 

7-2 

-  31.0 

-f22 

21  1 

Sept.  12 

23     58     26.0 

4 

47 

-   57-4 

+ 

16.  y 

58 

42.9 

59 

18.0 

-   35.9 

+    4 

4 

1 

17CH),  Dec.  24 

23     ?7     20.2 

4 

II 

+     2.y 

- 

1  .2 

57 

19.0 

57 

53- 

-  34.0 

-23 

26  j 

1710,  Fel).     ij 

23     51      59- S 

5 

6 

+  .J8.i 

- 

17.8 

51 

42.0 

52 

17.0 

-  35.0 

-14 

43  i 

July  22 

23     56     56.7 

5 

3 

-  29.7 

+ 

7.0 

57 

3-7 

57 

35-0 

-  31-3 

4- 20 

20 

Sept.  13 

23     53     51.3 

4 

41 

-    57-5 

4- 

16. q 

54 

8.2 

54 

47-5 

-  39-3 

+   3 

5*1 

Dec.    4 

23     52     17- 

4 

10 

-   20.3 

+ 

8.1 

52 

25.1 

53 

I.O 

-  35-9 

—  22 

'4  ' 

1711,  Sept.  15 

23     5"     39-5 

4 

If) 

-   57.8 

+ 

17.0 

50 

56.5 

51 

33-2 

-  36-7 

+  3 

1 
'3  ! 

1714,  Mar,  16 

23     57     57-2 

4 

44 

+   59-2 

- 

18.7 

57 

38.5 

—   I 

48 

Mar.  20 

23     57       q.o 

6 

1 

+   59-3 

- 

ig.2 

56 

49.8 

57 

28.5 

-  38.7 

—  0 

13 

1715,  May  26 

0       I     32.1 

4 

42 

+  26.4 

- 

8.0 

I 

24.1 

2 

I. 

-   36.9 

+  21 

3 

July  26 

0       0     13.3 

4 

34 

-  32.7 

+- 

7-5 

0 

20.8 

I 

0.0 

-   39-2 

+  19 

33 

Sept.  16 

23     56     44.5 

■» 

27 

-   57-9 

+ 

■7.3 

57 

1.8 

57 

43- 

-    41.2 

+    2 

50 

Nov.    3 

23     59     57.9 

4 

5 

-  47.2 

+ 

«7-4 

0 

15-3 

0 

50.5 

-   35.2 

-14 

56 

RE.SEARCIIES'ON  'TUF.  MOTION  OF   IIIF,  MOON. 


157 


Itivesli^alwii  of  Conn'wns  h>  tlie  l\ins  Qiiailiniil,  1706-1758 — Continued. 


Date, 

<  inrK-umi;  01 

Mean  of 

Com'spninlin.i; 

Alliliules. 

km        i    , 

Muan 

Ir)i(.rvat. 

h     m 

iliiiiily 
Motion  of 
Sun's  Off . 

H 

Coir.  Inl 
Motion. 

i 

<'lo,l< 

Tran 

M.-i 

III 

-tunc  0 
.il  over 
()ian. 

.r 

1717,  Sept 

20 

23 

55" 

48.7    1 

4 

20 

-   58.4 

+ 

17. f. 

5f> 

<K^ 

!)(•(. 

10 

1) 

0 

38.0   ' 

3 

5? 

-     3.0 

\ 

I  .2 

(t 

39-2 

l7lS,Sei)l 

27 

•J  3 

5'( 

,S.7 

4 

15 

-    53.5 

+ 

IH.2 

59 

2b  A) 

1720,  May 

31 

0 

f> 

Ifi. 

4 

42 

-i-    3".o 

- 

f).8 

0 

9-2 

May 

28 

23 

'>'\ 

4. 

4 

33 

■+    23.  s 

- 

5..' 

58 

58.7 

1727,  Mar. 

3  1 

23 

5') 

->2.2 

U 

0 

+    5').  3 

- 

I.J. 2 

59 

3.0 

1728,  Feb. 

13 

23 

53 

IC). 

4 

12 

4-   50.2 

- 

1S.2 

53 

0.8 

Auk 

30 

23 

4*< 

11,. 5: 

2 

7 

—    54.0 

+ 

13.8 

4S 

33.3 

«755.J»ly 

18 

0 

S 

7.7 

5 

54 

+ 

f>.5 

■S 

14.2 

1756,  Dec. 

13 

0 

1) 

2;  .2 

5 

33 

-     9.2 

+ 

3.7 

9 

249 

Dor. 

17 

-     4.6 

175a,  Jan. 

24 

i) 

22 

6.2 

5 

2 

+    36.4 

- 

14.2 

21 

52.0 

■:io(k 

-linu.  of  t 

fransii  over   1 

^)iiailrani.      ' 

i 

m 

s 

56 

45.0 

I 

12.5 

0 

10.5 

0 

45.0 

59 

35-5 

59 

44.2 

53 

45.0 

49 

17.2 

8 

10. 1 

9 

31.2 

22 

2.0 

Corr,  of    Snn's  De- 
Oiiadrant.  1  linalion. 


-  38.7 

4-    I 

5 

-  33.3 

-23 

2() 

-  43-6 

34 

-   35.8 

(-20 

■7 

-   36.3 

+  21 

33 

-  41.2 

■r    " 

8 

-   44-2 

-13 

31 

-   43.9 

-t-    8 

52 

+     4-1 

-     f'.3 

-23 

13 

. 

-23 

24 

-19 


It  will  be  seen  tliiit  tlii'  serio.>i  of  ofcultiitions  which  wo  use  beffiiis  nine  nioiitha 
before  the  iirsf  detenniiiiition  of  the  error  of  the  quadrant,  and  that,  diirinf--  the 
interval,  the  olistn-ver.s  used  a  forroction  for  deviation  nnich  .smaller  than  that  found 
from  and  after  1706,  May  14.  'There  is  no  way  of  determinin<>'  whether  there  really 
was  il  change,  or  of  dec,idin}>'  liow  the  value  actually  used  was  obtained.  1  am  strongly 
inclined  to  suHi)ect  that  tlu;  value  actufdly  used  was  the  result  of  some  old  determina- 
tion, which  was  fountl  to  be  erroneous  when  equal  altitudes  began  to  be  regidarly 
observed,  and  that  the  new  value  shouhl  be  used  from  the  begiiming  of  the  series. 
What  has  been  tlone  is  to  makts  the  reductions  on  each  hypothesis  in  order  that  the 
results  might  bo  comi)ared.  , 

The  deviations  of  the  quadrant  resnlting  from  the  observations  vary  with  the 
time  and  the  declination  in  a  niiinner  which  does  not  seem  reducible  to  any  e.xact  law. 
T  have  therefore,  in  determining  dock-corrections  from  the  several  transits,  tried  to 
execute  a  sort  of  double  interpolation  of  the  quadrant-error  from  observations  each 
side  of  the  date  in  time  find  each  side  of  the  declination  in  altitude.  The  con-ections 
thus  deduced  are  »\w\\  u  in  the  following  table  of  individual  dock-corrections. 

Instead  of  discussing  each  clock-correction  separately,  as  in  the  former  series  of 
observations,  I  have  in  this  series,  owing  to  the  uniformity  of  the  processes,  collected 
all  the  individufd  residts  into  ii  single  tiible.  Generally  at  least  one  determination  is 
made  on  each  side  of  the  time  of  observing  the  occultation,  and  the  correction  for  the 
time  of  observation  is  obtained  by  a  simple  interpolation.  The  table  is  as  follows,  and 
scarcely  seems  to  noeti  explanation.  It  may  be  remarked  that  the  cidumn  "^letm 
Time"  gives  the  mciiu  tabular  time  of  transit  of  the  sun  over  the  true  meridian,  and  is 
simply  the  equation  of  time,  subtnicted  from   24''  o'"  o"  when  negative. 

The  clock  of  which  the  corrections  are  here  given  Mas  the  "pendule  superieure"; 
most  of  the  occultations  were  actually  observed  with  another  clock,  designated  as 
"pendule  inferieure",  whidi  was  conqjared  with  the  other  soon  after  the  occultation. 


158  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Computation  of  Clotk-corrections  from  Transits  of  the  Sun  obstn<ed  at  the  fUris  Observatory, 


Dale. 

Clock-titne  of 

Tr.-iiisit  over 

Quadrant. 

Correc- 
tion. 

Transit  over 
True  Mcrid. 

Mean  Time. 

Apparent 
Clock-cor- 
rection. 

/t 

tn 

i 

s 

m 

/ 

m 

J 

m 

s 

1705,  Aug.  3 

33 

58 

49.5 

-    13(?) 

58 

36.5 

5 

32 

+  6 

56 

1)4 

3 

0 

5-5 

-  13 

59 

52 

• 

• 

• 

S 

59 

8.2 

•   • 

57 

55 

5 

27 

+  7 

32 

Srpt.  3 

83 

56 

33 

-  2I(?) 

56 

12 

59 

24 

+  3 

12 

4 

55 

23 

55 

2 

58 

46 

+  3 

44 

1706,  Jan.  31 

33 

59 

45 

-  I7(?) 

59 

28 

11 

57 

+  12 

29 

84 

59 

iS 

59 

I 

12 

43 

«3 

42 

a7 

58 

38 

. 

58 

21 

•  3 

23 

«5 

3 

38 

59 

23 

•   ■ 

58 

II 

13 

34 

+  15 

33 

Apr.  SI 

n 

57 

6 

-  ifi(?) 

56 

50 

58 

36 

+  1 

46 

as 

56 

37 

•  ■ 

56 

21 

58 

23 

+  2 

3 

May  34 

33 

56 

40 

-  31 

56 

9 

5^- 

13 

+  0 

4 

36 

56 

3 

•   • 

55 

31 

56 

24 

+  0 

53 

Nov.  16 

33 

59 

53 

-  35 

59 

>7 

45 

' 

-  '4 

to 

«9 

59 

26 

58 

51 

45 

45 

-  13 

6 

1707,  Apr.  4 

. 

50 

9-7 

3 

.2,4 

+  13 

2.7 

S 

23 

50 

1.5 

-  36.5 

49 

25.0 

2 

54 

+  '3 

29 

Sept.  3 

33 

55 

7 

-36 

54 

31 

59 

15 

+  4 

44 

5 

53 

44 

•  • 

53 

8 

58 

36 

+  5 

23 

1708,  Feb.  33 

23 

57 

26.5 

-  35.0 

56 

5'. 5 

'3 

57.2 

-1-  17 

5-7 

84 

' 

• 

56 

8.9 

13 

48.4 

+  «7 

39.5 

Sept.  5 

*3 

56 

26.5 

-  37-0 

55 

49.  5 

58 

21.5 

-*-   3 

33 

7 

54 

31-5 

53 

54.5 

57 

41.8 

+  3 

47 

1709,  Apr.  30 

*3 

54 

27 

-  36 

53 

51 

58 

46 

+  4 

55 

31 

53 

50 

53 

14 

58 

32 

+  5 

18 

Sept.  13 

23 

52 

>7-5 

-  35 

51 

42 

55 

44.1 

+  4 

3 

14 

5t 

33.0 

50 

48 

55 

23-4 

-   4 

35 

15 

50 

36.0 

49 

51 

55 

2.5 

5 

II 

16 

49 

3>-5 

48 

56.5 

54 

41-7 

5 

45 

])  16 

10 

25 

5 

24 

30 

30 

33 

+  6 

3 

30 

33 

59 

33 

58 

57 

53 

18 

-  5 

39 

33 

56 

50 

56 

"5 

52 

«7 

—  3 

58 

1710,  Dec.  4 

. 

. 

. 

52 

25 

50 

38.5 

—  I 

46.5 

5 

33 

52 

59 

-  -Kt 

52 

23 

51 

3-4 

—  I 

19.6 

i7ll,Sept.3g 

33 

55 

2r 

-   37 

54 

44 

50 

26 

-  4 

18 

J  30.6 

14 

54 

23 

53 

46 

50 

14 

3 

32 

Oct.   3 

53 

0.5 

•  • 

52 

33 

49 

29 

—  2 

54 

RESKARCHES  ON  THE  MOTION  OF  THE  MOON. 
Campii'iUioH  of  Clock-con eclions,  etc. — Continued. 


IS9 


Diilf. 

1 

CInck-tiinc  of 

Transit  over 
^Juadranl. 

Correc- 
tion. 

Trana 
True 

IH 

It  over 
Mcriil. 

Meat 

Time. 

Apparent 
Clock-cor- 
rection, 

1 

h       m     J 

1 
s 

s 

m 

s 

m     t 

I7ia,  May  15  j 

024 

-  33 

1 

3' 

55 

52 

-     5     39 

17  1 

2     37 

{ 

2 

4 

55 

54 

—     6     10 

1714,  Mar.  31 

23     57      1'' 

-   39 

5f< 

37 

7 

28 

+   10    51 

23  , 

57       5 

1 

56 

36 

7 

10 

+    10    44 

Apr.    6 

0      0    38 

-   39      ! 

59 

59 

3 

31 

+     2     33 

"1 

0    II 

59 

32 

■ 

56 

+     2     24 

i7i5,Ji'ly  21  ; 

0      0    45 

-   38 

0 

7 

5 

44 

+     5     37 

33 

0    48 

•      ■ 

0 

10 

5 

48 

+     5     38 

Aug.  9 

0      0     16 

-  40 

59 

36 

5 

4 

+     5    28 

10 

0      7 

• 

59 

27 

4 

56 

5     29 

16 

23     58     57 

58 

'7 

3 

sft 

+     5     39 

Oct,     7 

23     58     18.5 

-  39-5 

57 

39 

47 

59 

-     9    40 

10 

58     34.5 

57 

55 

47 

10 

-  10    45 

Dec.  33 

0       I     27 

-  34 

0 

53 

59 

30 

-     I     23 

30 

4     37 

4 

3 

2 

58 

-     I      5 

1716,  Jan.     7 

0       7     59 

-   34 

7 

25 

6 

4' 

-     0    44 

1717,  Sept.  35 

23     58     45.5 

-   39.0 

58 

6.5 

5> 

34.6 

—     6     33 

s6 

58     21.2 

57 

43.3 

51 

14.6 

-     6    28 

1 

1718,  Sept.    8 

0       I     24 

—  4' 

0 

43 

57 

30.8 

-     3     H 

10 

0     34 

59 

53 

56 

50.3 

-     3      3 

I7lg,  Apr.  22 

23     58     49.5 

-  41.5 

58 

8 

58 

25.8 

+     0    18 

23 

58     27.5 

57 

46 

58 

131 

+    0    37 

Oct.  29 

0      0     50 

-40: 

0 

ID 

43 

58 

—    16      13 

30 

0     33 

• 

59 

53 

43 

55 

-    15      58 

Nov.  36 

23     58     32 

-   37: 

57 

55 

47 

37 

—   10     18 

* 

27 

5S     38 

58 

1 

47 

57 

—  10      4 

1720,  Apr.  16 

23     59     52 

-  40 

59 

12 

59 

38 

+    0    36 

30 

58       7 

57 

27 

58 

42 

«     15 

33 

56     51 

56 

II 

58 

4 

+     J     53 

1727,  Sept.  6 

23     48     44 

-  42 

48 

2 

58 

15 

+  10    13 

8 

47     "3 

46 

31 

\     57 

35 

+  11      4 

1738,  Jan.     2 

0      4     52 

+      2 

4 

54 

4 

40 

-     0    14 

3 

5     46.5 

•       • 

5 

48.5 

5 

7.8 

—    0    41 

Dec.  23 

0     16     18.5 

16 

20.5 

59 

39-3 

—  16    41 

24 

16     54 

16 

54 

i      0 

9-3 

-  "6    45 

1739,  Feb.  13 

. 

4 

57-3 

14 

43-6 

+     9    46.3 

16 

0       4     58.7 

+      J. 5 

5 

0.2 

14 

34-9 

+     9    34-7 

i6o 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


More  observations,  from  the  anonymous  registers,  accidentally  oniitteil  l)efore: — 

Occultrttion  of  .lupiter,  July  27,  170... 
i''   22'  34"     '.)n  jnge  qu'il  tonclioit  par  lit  lunette  ie  8. 
I     22    40      il  comnieiicja  A  toucher  le  bord  de  I'D  par  la  lunette  de  18  pieds, 

1  24     3      je  crois  I'avoir  perdu  de  vue. 

2  6    26       U  est  sort  il  moitie. 
2      712       U  tout  sort. 

Tiansits  of  ©,  etc. 
I.  H. 

0  >r.  II  58  55A  I'  II" 

58  52  18 

58  48  12 

58  4oi  o    55 

58  38  o    52 

He  applies  a  correction  of  —  12"  for  instrument,  but  I  ciinnot  find  on  what  this  co  rection 
depends.     I  find  no  data  for  such  a  correction  till  December  30,  a.  m.,  when  we  find: — 
8  2  27,  haut  du  bord  suj*.  du  .soleil  par  M.  d.  ('.     i^  7'  o". 
8  6  39,  le  bord  inf.  a  la  inesme  hauteur. 
Thermometer  25.    Bar.  277A. 

r.y  rough  exau)ination  of  the  temperature  at  ditferent  seasons,  the  thermometer  .seems  to  be 
that  of  Fahrenheit.     The  observed  trans.'ts  of  O  stre: — 
Cent.  Midy. 

Dee.  25     o  4  7.3        o  3  50.3 
30    o  5  4.5        04  47. 


J11I.V  25 
26 
27 
38 
29 


c. 

,Mi<ly. 

12   0  i\ 

"  59  52 

12   0   0 

59  48 

«i  59  55 

59  43 

59  47!( 

• 

59  45 

59  33 

>  80  it  seems  he  now  applies  —  17"  for  error  of  instrument. 


It'  this  observation  is  worth  rediicinj^-,  it  is  nitlior  to  be  ii.seil  for  deternuiiiiif^  tlie 
position  of  Juj)iter  than  that  of  the  moon,  'i'he  observetl  ahittidc  of  the  sun  give.s  a 
ciock-oon-eetion  of  —  i'"  41",  wiiicli  is  entirely  ineoinpatibU'  wi.h  tiiat  derived  fntni  the 
tnnsits.  The  only  eoiir.se  seems  U>  be  to  aecept  the  times  of  apiiareiit  noon  j^iveu  by 
the  observers,  and  correct  the  ohjoks  accordin<,dy.  The  apparent  times,  deduced  by 
np])lyiii<,^  a  elork-correction  of  +  i  7",  are  jfiven  in  the  >[iMiioirs  of  tln^  Academy  for 
1 704,  page  233. 

1705,  Aug.  5.     (Aug.  4.6,  astron.  time.) 

3''    16'  40"     Inunersion  de  I'etoilo  dans  la  lune  par  la  'nnette  ile  17  [lied.s.    Je  n'ay 
AiUI  I    52  pas  pu  voir  avec  la  lunette  de  1 1  pieds. 


3 

18 

32 

9 
9 

5 
S 

0  pend.  sup 
8  pend.  inf. 

Uh 


after  the  occnltution. 


08 
Aug.        0  tr.  1 1   58    o"i 


3    ©  tr.  II  57  43 


o'   IS" 


"   59    S 
'3 


"   58  55     "'"''.v. 

59    56       58  49i 

'3 


1 1   58  36^  midy. 

II  58  16    midy  (convert). 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


i6i 


ic 


II  58  50 
'I  57  li 

D! 

I  21 
59  15   •  • 

58  54   .  • 

.  .  .   II  58  8 
'3 

II  56  41 

'I  57  SS 

•  •  ■  II  57  47 

16 

II  57  31 

No  altitudoH;  no  telling  liow  quadrant  was  corrected. 

The  interval  of  six  hours  between  the  observation  and  the  comparison  of  clocks 
renders  the  time  more  uncertain  than  usual,  the  difference  — 8'  being  assumed  constant 
for  this  time.  The  transit  of  the  moon  might  be  utilized  for  the  dock-correction,  but 
has  not  been.     The  results  for  local  mean  time  of  occultation  will  be: — 

Using  Oas.sini's  correction  of  quadrant,  Aug.  4,    is""  23'"  58"       .  ^ 
Using  ~35' 15''  24'"  20" 

>     .  1705,  Sept.  2. 

II  46  11;  itorl.  inf.  Futoile  r  de  la  5'  grandeur  dans  la  Janibe  uriental  du  Verseiui  entre  dans 
la  piirtie  obscare  de  la  lune. 

051     o  riiorl.  sup. 
o  51  39  I'liorl.  inf. 


o  47  37  IV'toile  sort. 
Sept.  I 


0  tr. 

11  56  0 

"  55  28 

58  12 

57  38 

'I  57  6 
20 

0  tr. 

II  56  46 

I"  56  33 
21 

niidy 

2     o    pendule  sup. 
2  38    pendule  inf. 


II  56  12     luidy. 


Sept.  } 


o  38 
0  tr.  II  54  18 


56  29. 


The  hour  of  the  last  olock-comparison  cannot  be  determined. 

1706,  Jan.  23,  p.  ni. 

II     o  14  I'^toile  entre  dans  la  partie  obscure  de  la  lune  par  la  lunette  du  17  et  par  cctte  de  1 1  p. 

22  36  I'etoile  entre  par  la  lunette  do  II  p. 

23  19  par  cette  ile  17. 

II  32  29  I'etoile  petite  qui  est  entree  la  derridre  sort  de  la  lune  17  p. 

32  34  par  la  lunette  do  12  p. 
II  38    3  pendule  inf. 

38    o  pendule  sup. 
Les  observations  pr^ci^dentes  de  la  3>  ont  e8t6  faites  &  la  pendule  inf. 

Jan.  274,  1706. 

12  21     3  l'6toile  i,  entre  dans  la  lune  du  cott^  de  la  partie  obscure. 
12  25  22  pond.  inf. 
12  21    o  pend.  supr. 
21 75  Ap.  2 


|62 

:>.,■■ 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

I.                             II. 

1706,  Jan.  21      0  tr.      n   5836                 054 

n  59  45 
17 
II  59  28  midy. 

44                          58     8i                 0  28 

26     <£    tr.      10  22  45                 25     4 

27      0             11   57   28                  59  49      , 

d            II    17     8                19  27 

aS                 II  57  19              59  38 

II  58  29 

1. 
II  58  12  midy. 

On 

January  23,  the  first  inunersion  isof  w'Tauri 

the  next  two  ai)i)ear  to  be  two 

observations  ot"  the  iunnersion  of  >r  Tanri.     All  the 

observations  are,  however,  dis- 

conlaut 

in  a  way  which  yives  rise  to  the  susi)icion  that  an  eiTor  of  3"  was  made  in 

the  com 

parison  of  clocks. 

1706,  April  21.     Occnltatioii  of  ij 

Leonis. 

»  59  «5 

Immersion  de  I'eloile  derriere  la  lime  supr.  peiid. 

9     «  45 

Iniiiiersion  ile  IVioile  r,  diiiis  le  col  dii  Lion  avee  line 

lunette  de  3  pieds    .    .    .  pend.  inf. 

9     «  47 

avec  line  lunette  de  2  pieds. 

920 

pendule  supr. 

9     4  28 

pendnle  infr. 

9  55  20 

Kuiersion  de  I'otoiie  1;  de  la  lune  par  la  liinett<!  tie  16 

pieds  exiuite,  pendule  inf. 

L'tttoile  en  entrant  dans  la  lune  iii'ii  parn  s^tllonger  esiant  vue  dans  I'axe  de  la  lunette  de  16. 

pieds. 

Aviil  19      Q  tr.     II  57  12  (sic). 

59  '*  (8'c)- 

20                         56  3' 

58  41 

. 

■        21                        56     I 

58  12 

» 

/          '■%        22                        55  32 

57  43 

23                     55    3        : • 

57  H 

May   II                   '«  57  38 

59  52     2'  ajout6. 

V     "                       59  '4 

«  30 

»4                        5835 

0  49 

•s                  — 

0  3' 

Altitudes  of  Q,  .Ma.v  14. 

• 

9I'    47'    45"                         2>'     12'     11"                         50°       0' 

040    pend.  su]i. 

50      16                                       9      36                            50       20 

0     4  37     pend.  inf. 

52      50                                       71            ■               50      40 

55-9                           4    30                   5'       ° 

58      8                           1    46                   51      20 

9     47    45 

14     12    II 

4     24    26 

2     12    13 

>'     59    .58 

. 

8 

II     59   50    midy  tl  la  pendule  inf. 

37 

II     59    13    midy  &  la  pendule  supr. 

'"-  S9_4_* 

0    29     d<-elinaison  de  I'instr. 

May  14 

11     59    4» 
«5 
II     59    27     uiidy. 

This  calculation  refers  to  the  transit  of  May  14. 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


163 


1706,  May  24. 

10  51    29    Ij'6toile  eiitre  dans  le  bord  tie  la  J).     Lu  luiie  sp  couvre  I'etoile. 

11  3    S3    pend.  inf.  10  51  39  (sic) 
II      00    pend.  8upr.  3  53 


10  47  46 
3  48 


10  51  34 
TrausitH  and  calciiiutiouN  t'ur  clock. 


May  23 

0             iio  55'  50" 

58'     6" 

56' 

58" 

24 

0                    55   32 

57    49 

56 

40—20 

56  20    rnidy. 

«4 

Id                     9    52     41 
I/ctoile            9    55     39 

3  40 

»S 

,d             10     34    43     Dl 

10     36  49 

9  55  39 

26 

O'             II     57    10 

20 

Aug.    I      © 


II       56        2 
20 

n     55    42 
II     54    52 


9  55   «9 
3  48 

9  59     7 


57'  6" 


II  59  3°     pond.  8upr. 
II  44     5     pend.  inl'r. 
15  25 


Altitudes  0   Aug.  i. 


8  26 

30 

2  53 

II 

6  26 

41 

3   >3 

204 

«■   39 

504 
10 

II  40 

04 

«5 

25 

"  55 

25 

inidy  X  la  supr 

I'  55 

59 

8  26  30 

-  53  'I 

40  50 

28  38 

5'     4 

41    10 

33     2 

46  38 

41   50 

35     8 

44  32 

42   10 

34      dC'clinaiMoii. 

1706,  Nov.  r8  a.  in.,  174  ast.  time, 
o  II   59     pend.  inf.     L'etoile  h« cache  de  derhere  In  5  en  ligne  droitc  avecCopernic  et 
o  17  30    pendnle  aup. 
o  18  25    pendule  inf. 


o  55 


Nov.  16      0  tr.     II  58  43 


II  59  52 

3° 


"7 

Id 

9  52  25 

54  35 

le  vent. 

II  59  22 

'9 

© 

II  58  17 

II   59  26 
34 

II  58  52    inidy. 


164                                          RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Sept.  19 

'»  58  35 

0  43 

"  59  39 

II  59    4    from  alt. 

35    '!«*'•• 

Alt.   0   Sept.  19,  1706. 

9    27    24                2 

JO    6 

33     0 

"        31     40 

25  .53 

33  30 

35  57 

21  36 

34    0 

l)fc.    5,  lyo*'. 

9  39  40           2 

18    3 

12  40 

43  35 

14  13 

,    '3    °            : ',' 

47  23 

10  19 

13    20 

»7°7) 

April  4. 

S""     8'   r"     pL'udule  siipr. 

La  petite  etoile  /> 

d'Aries  est  cachde  par  le  bord  obscure  de  la  lune.                     | 

mill       10    6 

9     7  41     peiul.  iuf. 
8  54     0     peiul.  sup. 

Apr.  I 

3      0 

5'   5'4                 54     I 
tr.  II  50  28J               52  48 

49  43                  5'  52 
48  57                  S'     6 

«3  4« 

Apr.  4 

4 

5 
Alt.  ©. 

9  33  " 
36     7  duh. 

38  59 

4'   57 

2     7  41 
4  49 

I  S3 

«  58  56 

38  10 
38  30 

38  5° 

39  10 

9  33  " 
2     7  41 

4  34  30 

2  17  »S 

II   50  26 

«6 

II   50  10 

1 

11   50  47J 

37      diff.  declinatio. 

1707,  June  18 

©     II  55     8 

'      57  25 

S6  i6i 

»9 

54  53 

54  37 

June  19. 

57  " 
56  55 
Altitude  G. 

56    2 
5546 

9     2 

4 

37 
48 

48  26 
46  17 

48    0 
48  20 

•             7 

0 

44     5     '' '''" 

48  40 

9 

II 

41   54 

49    0 

II 

23 

39  4« 

49  20 

'3 

36 

37   29 

49  40 

From  all  which  he  seems 

to  deUuce  a  correction  of  —  30"  1 

""or  his  instruments. 

I 

707,  Sei)t.  3.     <M 

ultation  of  Autares.                                                                       | 

7''  45'          Ant^ires  entiedans 

la  partie  obscure 

de  la  lune  pend 

inf.     (.lette  immersion  n'a  6t6  ob-                     1 

servee  qu'a  quehpies  secondes  prb*.                                                                                                       1 
8    33    II     Antnres  sort  de  la  partie  claire  de  la  luue  pur  la  lunette  de  (Jampani,  exaute.                                       | 

Then  come  the  following 

calculntions: 

8*  50'            I'horl.  sup. 
8    52    57      I'horl.  inf. 

7"  45' 
5    304 
'34 

8  33  " 

5  30 

'5 

■  ■"■". 

7     5°    44 

*      57 

iV  retr. 

8  38  564 

2  57     a  rotr. 

» 

• 

» 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  1 65 

7  47  47    Leure  v6r.  de  I'iinni.  d'Aiitaies. 

8  36    o    heure  v6rit.  de  I'^iuers. 

Traiisits  of  ©.  Altitudes  ©  Sept.  6. 

Aug.  29  II  57  25             S9  34  58  ^9-5                            9  3»   ^3  o^  °  2  »4  S^ 

30  58  55  .  34    9  38  20,  22  II 

31  58  18  •  36  48  38  40  19  28 
Sept.   I  57  36  39  37  39  o  16  38 

3      II  54    3  56  '2  55     7i  42  26  39  20  13  49 

I  58  40  o  48  59  44 

■       fi      ,     57  S6J  05  59    0.8 

f  57  «2  59  20  58  16 

No  atiiteinput  when  the  clock  was  put  forward. 

Tlie  unthors  of  tliiH  "register"  Honietiines  failed  to  apply  any  correction  for  mo- 
tion of  the  Hun  to  their  corresiwnding  altitudes. 

The  clock  seeni-s  to  have  been  put  forward  six  minutes  before  the  transit  of  the 
sun  on  September  5.     Snl)tracting  this,  the  clock-corrections  from  the  transits  are: — 

Sept.  3.  Sept  5. 

Clock-tinu'8  «>f  transit  by  quadrant      .     .  23''  ss"     7^'  23''  53'"'  44" 

Con-ections  ol  quadrant —    36.J'  —    37' 

Clock-tinies  of  true  transit 23"  54'"  31"  23"  53™     7" 

Mean  times 23"  59"  15"  58""  36" 

Clock-corrections -f   4"'  44"  -f-   5"'  29* 

Subtracting  2'"  57"  for  reduction  from  one  clock  to  the  other,  the  times  of  the 
phases  are: — 

Iiuuiurtiiun.  EnierHioii. 

Clock-times  of  occultation  of  Antares,  1 707,  Sept.  3,  7''  42'"  3':  S*-  30"   14" 

Clock-corrections +  4'"  5''  +  4"'  52" 

Paris  mean  times •.     .  7"  46™  54":  8"  35'"     6" 

Greenwich  mean  times     .     .     .     •     .     ►     .     .     •     •  7"  37"'  33*:  8"  25"'  45" 

The  first  time  may  be  considered  as  affected  with  a  probable  error  of  at  least  10". 

1708,  Feb.  23,  p.  m.    Occultation  of  Venus. 
7    o  31     ?  commence  a  entrer  i^  la  pend.  inf.     Lunette  de  34. 

o  46    Kile  entro  entiiirement  dans  la  lune. 
7    o  23     9  commence  ii  toucher  la  luue  par  la  lunette  de  34. 

038    V6nu8  eutre  enti^rement  A  la  lunette  do  34  et  de  12  pieds. 

.  »dd     3'  19" 

7  16  o  i)eud.  supr.         Feb.  21  ©  tr.  11  57  45  59  57 

7  16  9  pend.  inf.              22  57  4  59  '5 

33  56  20  58  33 

•             9                     H  ■       ■   55  38  57  50 

25  54  49  57  « 

Feb.  24.  Alt.  ©. 

g^  42'  45"      .-       10'  6"  24O  so' 

46  8       "         6  jg  25  ,0 

49  42  3  «3  25  30     ^ 

S3  «6  S9  3S  *5  50 

56  ii  >  55  »7  »6  »o 


1 66 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


1708,  Sept.  6. 
Emersion  de  x  Taurcau  de  la  partie  obscure  de  la  Itine. 
peiidiilo  inf. 


9  32  S> 
1070 
1070    pendule  supr. 


Sept.  3 


000 
0  tr. 


'«  57  15 


59  24 


9  50  52 
33  48 
40  38 

43  33 
46  3' 
49  29 
52  35 
55  38 


Sept.  12. 

26    o 

23  13 

2  16    s 


[I  58  19J 
34 


1'  57  45 

4 

II  56  19 

58  29 

11  57  24 
34 

II  5f  5° 

S 

II  55  22 

57  31 

II  56  26 
34 

"  55  52 

7  a.  in.  1 
7  ©  tr. 

1  cent.  5  14  23i 
"  53  27 

15  42i 

55  36 

II  54  31} 

9  ©  tr 
12 

•I  57  58i 
II  58  14J 

0  16 
0  23 

34 

July 
Sept. 

'I  53  57i 

1708,  J 

Illy  9. 

Alt.  0. 

9"  37'  4" 
39  27 
4«  5' 
44  »7 
46  41 

19'  57" 
17  36 

15  '3 

12  50 

2  10  23 

51°  50' 
52  10 

523° 

52  50 

53  10 

II  58  3ii 

7 

II  58  38* 
■I  59  6J 

midy. 


midy. 


midy. 


28    decl.  ad.  occid. 


35  40 
^6     o 

36  50 

37  10 
37  30* 

37  50 

38  10 
38  30 


1709,  April  20. 
7'>  52'  49"    Immersion  dans  la  luue  de  I'ctoilu  t  de  la  Lion.     Tend,  infer. 


10     18  30       pend.  inf. 
10    II    o      pend.  supr. 

7  30 


10  51  31  pend.  inf. 
44  o  [tend.  supr. 

7  31 


Apr.  19,  H.  m. 
4  30  10  p.  inf. 
4  24  o  p.  sup. 

6  10 

5  » 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


167 


Apr.  17     0  tr. 
18 

19 


"  SS  19 


S7  29 
56  S« 
56  II 


«i  SS  46 
3a 


'.      .  : 

II  SS  14 

ao 

II  .S3  22 

SS  33 

II  54  28 

»t 

«'  S2  45 

54  SS 

/ 

32 

•I  S3  56 

niidy 

^3 

"   5'   34 

S3  45 

II  52  39 
32 

'■;■■■•■       ■ 

II  52     7 

30 

33" 


II  SI  37  • 

1709,  September  17  (or  16J  probably). 

)\  I'iioil.  inf.    Imniernion  d«  I'etoile  a  de  la  5'  gruudeur  dans  la  partie  obscure  de  la 
lune.     Kile  otoit  en  ligne  droit  avec  H^lion  et  Timarcbus. 


0  23  51     riiorl.  iuf. 
0  13     0     I'horl.  aup. 

9  45  44 

1709,  Dec. 

24. 

12° 

20' 

49  47 

245° 

40 

10  s« 

Sept.  15     ©  tr. 
16 

II  49  22 
II  48  27 

5'  30 
50  36 

S3  59 
58  IS 

0   43 
56    27 

»3 
»3 

0 

20 

»8 
»4 

If'     k 

Ti»  pendule  superieur 
Dec.  24 

51    '3 

10  24     3 
p  s'est  arest^e. 

"  .=;9   4 

S3  24 
58  43 

1 1 

S3  " 

52  27 
26     2 

57  S3 
57  ^' 

(CI 
eel. 

r 

ord  qui  manque.) 

1710,  Feb 

9  '4  13        29   47 

•7  25        26   33 

■    20  37        23    23 

23  54     2  20      6 

17 10,  July 

9   '6   19         37    34 

r . 
22. 

•7" 
18 
18 
18 

47 

SO' 
10 

30 
5° 

30 

1710,  Feb.    9      1151   10 
July  22      II  56  27 

1 1 
1 1 

32  «1 

52   >7 
57  35 

II 

57     3 

20  51 
25  32 

28    23 

48 
48 

20 

SO 

• 

3» 

30   '4 
35     0 

23    39 
2   '8    SS 

49 

5° 

30 
10 

8  24  52 
28  53 
28  54 

8  38  34 
36     o 

2  34 

8  47  44 

9  ««  5' 
9  '4  24 

Sept.  20 

«3 


1709,  Sept.  23.    Ocfuitation  of  Pleiades. 
Maia  entre  dans  la  Inne,  lunette  de  17  p.  \ 
Talgcta  entre  lunette  de  34  pieds.  '  1 

Taigetu  entre  lunette  de  17  p. 
pendule  inf. 
pendule  supr. 


s 


pend.  infer. 


L'6toile  marquee  x  putre 
L'^toilo  X  sort 
Maia  sort 

O  tr.     II  58  28 
i«  55  46 


luuette  do  17  p.  peud.  iuf. 


o' 
57 


36" 
54 


56  50 
34 


II  56  16  midy  l«  2ad. 


,68  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

1710,  Deo.  4.    Occ.  Pleiades. 

45012    Electra  entre  dans  la  lune. 

7  36    retard  horl.  sup.  ab.  hor.  var.t 
6  12 

1  24    add.  ■  ' 

54822     L'<5toiIe  proche  d'Asterope  cache  par  la  grande  lunette. 

5  56  58    Asterope  entre  dans  la  lune  par  la  grande  lunette. 

6  9  50    ■}(•  sort. 

2328    Maia  sort  par  le  g.  lunette.  .  • 

6  59    9    pend.  inf. 
S3    o    pend.  supr.  * 

69  ,  "/'     .    ^ 

'  Alt.  ©  Sept.  13. 

Dec.  2   0  tr.   n  S«  59     54  21  9  29  6     18  4i  35°  S^' 

3   "  "   II  51  55     54  «6  3«  54     "5  48  36  10 

3  |(  "    9  56  58      59  4  34  45      '^  5«  36  30 

4  0"   II  51  io      54  12  37  41      'o  4  3^     3° 

4  !(  "    4  59  45    5  '  58  >  .-  . 

5  ©  "   II  SI  S3     54  S  Dec.  4- 

Sept.  .3         ..5343     5S52A-39'      -^^3,    ,„,     ,,Oo' 

51  44      —        14  *o 
11  52  17  +  8  =  11  52  25 

1711,  Oct.  I.    Occ.  Pleiades  (Oct.  0.6  astrou,  time). 

3  40  1 1     Maia  est  cach6e  par  la  lune 4^'  40" 

add  6'  19" 

48  10    Taigeta  est  cachee  par  la  lune 54   39 

4  50  55    Alcione  esl  cach6e  par  le  bord  olair  de  la  lune       ...        57    26 

6    31 

4  56  18    Maia  sort 5    *    49 

5  34  23    Alcione  sort 4°    55 

6     3J 

Alt.  0  Sept.  15. 

Sept.  27      0tr.     .155  53  58'      3"  9  36  5*  *    4  '6  36°  3°' 

28  I.  55     S  ^7     '6  40    o  I  24  36     50 

'   a^  —  56    26  4253  5828  37     10    Corr. +  17. 

45  59  55  «9  37     3° 

Oct.  0.6     Le  ventre  de  la  J      2  53    30  49    9  '  S»     S  37    5° 

Jl  SS     «6 

Oct.    2  II  51  56  54      5 

Sept.  IS  II  5°  28i  52    38 

Got.  2        II  S3      o 
32 

II  52  28    midy. 
Ue  seems  to  have  used  the  same  clock  with  which  the  transits  of  the  ©  are  ob8er^'ed. 


RESEARCHES  ON  THE  MOTION  OK  illK  MOON. 
1712,  Miiy  is'/j. 
II   22     2     Imiiioi'Hion  tliiii.s  lit  partiti  oU.'4(;uru  (1(>  liv  liiiie  (lu  ;  I. ion.     IVml.  iiil. 


169 


Auf.  35" 

0   I 

>S 

Emersion  < 

lu  ht 

Itiii'tic  cl 

iiie. 

1 1  26 

2 

pi'iul.  inf. 

II  27 

U 

poiKl.  )«-jp. 

M.iy  13  0  ti 

. 

I( 
0  0  29 

)| 
2  42 

0 

2  4 

'5 
»7 

0  0  57 

3  '« 
3  44 

32 

18 

°  I  45 

4  0 

0 

'  32 

"  Lh  19  May  iV  e,''  ilii  matin  Mail.  Oasttiiii  est  aucoiu-Jiru)  il'iiiiu  tillu  i|iii  a  6u'i  ba|iti.s6o  li>  27  ut 
nnininCtii  Hiisiniiu  Kraiiyoisu ",  wliiuli  perhaps  acU')iiiitM  tor  our  li.iviiii;  no  coi'i-a.-ip  >:iilin^  iltilinhtH 
Hiiice  last  8upteiiilier. 

17 14,  Jan.  19,  p.  III. 

S''  46'  18"     pond.  iif.     ImiiiRPsion  dans  I  i  (lartie  obscure  de  la  lime  il'iuu'  t'toile  de.s  PoiHSoiis. 
6    34     o      IV'toile  fMrt  do  la  [tartie  ulaire  de  la  luni'. 

55    10      uiK^  autre  <>toile,  buaiiuoup  plus  petite,  eiitre  dans  la  partie  ob.s<;iiic  de  la  luiic  vers  sun 
bord  sept.  <j«'elle  rase  presqne. 

1714,  Mar.  21. 

10  14  41     pend.sup.  uneetoile  «  (Tauri,  cornu)  entre  dans  la  J.  . 

3  28  . 


10  18  9 

Corr. 

•  0 

Alt.  Mar.  16. 

Mar.  19 

"  56  36 

58'  46" 

-38" 

9  27  2' 

28  27 

30  10 

20 

56  24 

58  33 

-38 

34  44 

21  7 

3«  0 

21 

S6  .1 

58  20i 

-39 

39  26 

'6  35 

3'  30 

22 

56  0 

58  10 

43  55 

8  55  36 
58  10 

2  12  3 

Mar.  20. 

2  58  42 

2  s6  8 

32  0 

27  40 

28  0 

1714,  Apr.  7,  a.  in.  (6.6  ast.). 

3  24  II     Immersion  of  ^  Sagittarii  (bright  limb)  pend.  supr. 
or  3  24  12 

4  37  27     L'etuiie  sort  de  hi  partie  obscure. 


add 


Apr. 

5 
6 
8 

0 

tr. 

XI  52  46 
II  59  6i 

0  I  43 
61  15 

9 

II  58  56 

— 

10  60  52 

11  II    58  32  60  42 
At  noon,  T.  S4°-i  i  barom.  27  i  ijj. 

22 75  Ap.  2 


(+  i'  6")  (cl.  adv.  7') 

(_  j'  5")  Apr.  10,  0  limb.  »u|ii-. 


6"  14' 

.4" 

40  0 

«7 

26 

3  3° 

20 

40 

3   0 

23 

55 

2  30 

27 

15 

2   0 

30 

27 

I  30 

34 

8 

I   0 

170 


ftuf.   o'  I)" 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

1715,  .Inly  22,  H.  in.,  Occ.  of  </(?)  Fisciiini  (21.6  aat.  time). 
2''  53'    2<>"     IininerHioii  en  III  lioril  cliiirt". 

J     S3    '7 

3     46    13       .I'liy  coinincMcc  <l«  voir  IVmersioii  de  IVtoilH  (»l)8mirp.     LVtoile  Ho\t 


3     4^' 


tMKtore  nHM'7.  HeiiHibU-  t|ii(ii<|ii'il  tit  cruiiil  jour. 

©  Alt.  Mi, .  26. 


Mh.v  26 

0"  0'  S3" 

l( 

July  20 

0  tr. 

"  59  .13 

I  48 

21 

59  37 

— 

22 

•    -■: 

59  40 

'  S6 

II   54  29     IV'toile  ;f  (111  Veist'iiii  entre  dans 

III  lllllC. 

•lib.  a'  37 

II  58  12     peiul.  inf.  .     ./ 

II  54    o     penil.  Mii|>. 
o  39  36    tiinersion  de  i't'tiiile  x- 
Jnly    26      0  tr.  11"  59'    52"*        2'    7"! 
AiiR.     9 
10 
16 
Sept.  15 
16 

'7 


9  36  S<5 

26  9 

50  20 

39  '7 

23  46 

50  40 

41  42 

2   21  22 

5'  ° 

44  9 

18  56 

51  20 

-  A  list.). 

3  Alt.  July  26, 

'7«5- 

9  39  '" 

20  59 

49«  40 

43 

17  19 

50  10 

46  51 

2  «3  37 

50  40 

59 

10 

1  22 

59 

I 

— 

57 

5> 

60  3 

57 

I 

59  8 

36 

39 

— 

9  34  4» 

38  5' 
43   «3 

47  49 
S'   -9 


Sept.  16. 

'8  55 
«4  36 
10  II 

5  39 

I      o 


.mm-  II    58   26 

1715,  Oet.  9,  p.  ni. 

gii  ,y/      2"     lY'toile  veiioit  d'fiititr  diuiM  In  liord  iiliw.  de  Irt  liine. 

I'end.  ill!'.     Liiiietti' tlo  17  p. 
8     24    22      ]i(>nd.  inf. 
8     23       o       pend.  sup. 


I     22 


jh  jg/    ,//  pend.  sup.     Iniinersion  de  IVtoile  x  "l"  Verseau. 
7     *3  37     |>end.  inf.      Iuiiri('i>ioii  de  I'ctoile  x-' 


0  tr. 


7 

»5  39 

penU.  tut. 

7 

30  0 

pend.  8up. 
Dee.  23 

30 

1716,  Jan.  7 

10 

0  0  15 

*  39 

0  3  26J 

5  48 

0  6  48 

— 

0  7  59 

10  20 

35   '° 

35  40 

36  10 

36  40 

37  - 


0 

Alt.  Nov.  3. 

Oct.  6 

0 

ir 

— 

60  37 

9  5°  44 

9  23 

20  20 

t 

II  58  14 

— 

9  56  10 

2  3  43 

20  50 

10 

'«  57  30 

59  39 

to  0  0 

59  5' 

21  K) 

Nov.  3 

'I  59  43 

■  58 
Dec. 

30. 

!>• 

4   2 
in. 

■  55  S' 

21  30 

RESEARCHES  ON  THI.  MOTION  OF  TIIF,  MOON. 


tyi 


1717,  Sept.  25.    (>i'<uiU.  of  AUlcWiiniii,  a  In  |U'ii(liile  iiif*>rieure. 
9   13  46    Alilebiiriiii  cHt  vmtM  \mr  In  liiiit'. 


Hub.  a'  14k" 


auf.  »'  16" 


9  JO  18     peiidiiU^  intV'riciirc. 
9  16     o     peiiiliile  Hiipt'i'lviirt', 


10  52  21     si^iiMl  pciiil.  inf. 
10  48    o    pciitl.  Hiip. 


4  18 


10    69    AUlelxiraii  sort  tin  bord  obHCure  tout  *l'ini  cuup. 

1717,  Dec.  19,  Alt.  0. 
Sept.  24      0  tr.     II  58     2  —  corr.  —  41" 

»5  "57  41         59  50  -4'" 

26  '■  57  «7i      59  25 

Dec.    19  001  2  24 

Sept.  20  if  55  4'        57  49 


9  53  7 

la  40 

57  26     3'  55" 

"3  0 

'°  '  3*    59  36 

13  »o 

6  -t   '55   9 

13  40 

17 1 7,  Sept.  20. 

9  41  23     »o  >3 

34  30 

44  3'      7   «o 

34  5° 

48  6  ilul).  4   1 

35  '0 

50  44      0  5' 

35  30 

a<l(l 


No  reciords  for  the  (irst  Hvo  inontliA  of  1718. 

1719,  April  22,  i>.  III. 
7  42  37     liiiineiKioii  (rAlilebaruii  tliiiis  la  lime  f\  lu  vne  et  en  ineanie  tempH  avecia  lunette. 

«  55  '-'.    ■     '^ 


7  44  32 

8  32  II     Aldebaran  sort  dn  liord  clair  de  la  lime, 

•  56 


8  34     7 

8  34  58  Aldebaran  sort  et  on  Papperi^oit  dans  riimtaiil. 

8  37    o  la  peudule. 

8  39  52  pend.  inf. 


2  52 

1718,  Sept.  26 

0 

tr. 

59  29 

■  38 

0  Alt.  Sept.  27, 

,7.8. 

*7 

59  6 

«  '5 

28 

58  39 

0  48 

9  48  19   2  9  58 

32°  30 

1719,  Apr.  22 

«'  57  44 

59  55 

(•orr. 

-42" 

51  31     6  46 

3'  5° 

»3 

57  22 

59  33 

-41 

54  45     3  33 

33  'o 

17 19,  Oct.  30,  Oct.  of  Aldebaran. 
9  58  57     a  la  peudule  sup.  Aldebaran  sort  ilii  bord  obscure. 


•lid  o'  13" 


1 7 19,  Oct.  29 

3° 
Nov.    3 

6 
Nov.  3 
Nov.  26 


0  tr. 


II   59  43  1'    57"  o     o  50 

I     40  40 

o  30     o  3?     13  

II  57  59  o     '5  o     o  10    inidy. 

8     3  58   —  dii  Verseaii  an  lixe. 


7  14  30     IVtoile  ,  I'll! re  ilans  le  disqne  de  la  luiie  claire  1.  7  J  p. 
7  14  54     lY'toile  r  •'''"•"  ''""'<  '»  '"'"'  l'"""  '**  ^»nftU-  de  17  |i.  apres 

avoir  paru  quelcpies  seconds  aur  le  bord. 
7  18     I     pend.  inf. 
18    o    |>end.  sup. 


172 


RESEARCHES  ON  TIIK  MOTION  OF  TIIK  MOON. 


170., 

Nov.  3.) 

ti' 

57'  '.V 

-5 

— 

zf, 

57  ^2 

27 

^^   28 

)!  • 

59'  .HJ 

S9  .^6 

59  4» 


1720,  Mii.v  21,  Alt.  ©. 


9  3>  57 

49  'o 

3S  3' 

49  40 

39  4 

2  21  2« 

5°  '° 

42  4< 

50  40 

S«  5° 

Sa  ao 

5»  49  30 
53  '9  2° 


1720,  April  -M,  n.  in.  (20.5  iist.). 

1720,  May  28. 
o  22   i|     pcriil.  iiil'.     Iiiiiii.  ;-'  \'ii(!iiii.s,  9  42  34  op.        2   15  34  op. 

o  22  4+  I'liM.  (!»' /' Viijjiiiis.  46  14  op.  — 

o  48  ifi     l':iiii'i>liiii  <li's  (li'iix  I'tdilcs  (III  liord  clair.  49  32  — 

S3  35  — 

o  25  48  |ii'Mil.  inf.       Apr.  16   ©  Ir.    11  58  46     o  57 

O  26  o  JO  —        59  '2 

*3  "55  45J  57  5^^  0,-42" 

o  12  Miiy  19  II  59     2            I   i7i— j'a  jouU' i' i\  la  ppiidnlo, 

o  55  4y  I'l'inl.  inf.                         ai                            59  37             i  53 

o  56     o  -              ti                             58  28             o  43 


1718,  Sept.  9. 
8''  41^'   44"     LY'toile  ilJHparoit  an  bord  ile  In  lnn«' — penil.  sup.  de  la  tour. 


10      9    33       pendiile  inf.  de  la  tour. 
10      9      o      peiidtiU' sup.  tie  la  tour. 


33 
Dans  la  tour  infi-rieiire.    (La  peiulnlc  retardoit  de  ntie  minute  6  aecoudoM  a  lY'gard  de  cello 
(Ic  lii  tdiir  Slip.) 

84630     I  no  t'jtoile  deH  I'oissoiis  s'eclipse. 


(I  see  nolliint;  to  reeoncili-  the  diMerepanciea  between  the  clocks.     IJere  is  everything: — ) 
Sept.    7  ®  tr.         II   54  46J  56  S7i 

54  19  56  29      J'ajoute  6'. 


8 


"   59  3° 


I  38 


'riicrc!  was  coiisideriililc  tliHiriiltv  in  reduciiij;  tlu'se  ohservatioiiH,  but  I  think 
I  Imvc  conipU'fcly  suriiKiiintiMl  it.  From  tlio  Memoirs  of  the  Academy,  i  718,  it  would 
seem  tliat  tlic  lir.st  of  tlio  above  observations  is  that  of  Makamii,  who  fj^ives  8''  45"'  35" 
for  the  aj)]iarent  time,  and  lieiiee  nnist  liave  ajudied  — 9"  for  (dork.  It  would,  there- 
fore, seem  that  this  "  peiid.  sup.  de  la  tour"  is  tiie  elock  with  whieh  the  sun'.s  transit  is 
re<;idarly  oliserved.  the  eorreetion  of  whi(di,  on  mean  time,  is  —3'"  6".  We  have 
therefore,  8''  42'"  38'  for  the  mean  time  of  oecultution  from  Mafai.di'h  observation, 
'i'he  equation  of  time  being— 2  57',  this  lesult  agrees  exactly  with  Mabalw's  as 
published 

The  lower  clock  u.sed  by  Cassini  being  ;i;i'  ahead  of  tiie  U[)per  one,  its  correction 
on  apparent  time  would  be  —42".  He  writ^>  43',  so  that  this  hypothesis  is  pnd»ably 
correct.     But  ho  actually  applies  50',  seemingly  out  of  carele».sno88  with  regard  to  the 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


'73 


iinitM  of  HecniidH,  hiuI  thuH  obtaiiiH  \m  printed  result  8''  45"'  40*.  Siipposiiifr,  then,  a 
(lifl'erenee  of  33*  between  the  ehiekn,  the  eorreetion  on  mean  time  wouifl  be  —3'"  3',)", 
and  the  mean  time  of  oeenltation  would  be  S''  42'"  51".  The  oceultiitinn  was*  observed 
jiIho  by  La  Hike^  and  tlio  three  resultH  nre: — 

Maiuldi 8"  42"'  38*.  ■ 

La  Hire 8"  42"' 44".! 

Cahhini        8"  42"' 51'. 

I  mn  inclined,  under  these  eireumstunces,  to  uho  La  11h{e'h  observation  only.  The 
moon  was  totally  eclipsed,  and  the  oceidtation  to«»k  place  at  a  ecmsiderable  auffle,  so 
that  the  results  with  respect  to  the  phase  of  the  moon  are  not  so  di.scordant  as  the 
times  would  indicate. 

1727,  Sept.  7.    Occiillutioii  of  I'leiutlfs. 

li'et.  lU'H  i>l(<ia«leH  f  litre  duns  le  boi-d  cluir  nvec  unu  I.  d.  15  |i. 
iivec  Itt  laiipttci  de  Angletorre. 

"  "        ♦'     6J  p. 

lA-l.  di'H  ricitidcs.    On  ii'a  pns  pn  la  voir  iivev  leH  2  uiitivs  luiictteH. 
LVt.  Ill  plus  sepleiitriuiiale  eiitit; 
47  uu  48  par  la  liiiietle  de  Aiiglcterre. 
FiVt.  Ill  plus  inerid.  uiitre. 

liUiiette  il(^  Aiiglcterre.  2  48  13    |ieiid.  inf. 

2  36    o 

pin-  la  liiiu'ttt)  de  6^  p. 

Kinersioii  de  letoilu  quo  je  (srois  la  1". 

Emersion  de  celle  «pie  je  croia  In  2". 

KuierHioii  de  celle  que  je  cri/is  la  4°.  4  n   12     peiid.  inf. 

Krnersioii  de  celle  qui  est  la  plus  iiit^ridionale.  3  59    o    P-  f^u)!. 


2' 

3' 

7' 

2 

3 

4 

3 

5 

2 

8 

56 

2 

4« 

5° 
47 

2 

44 

1 

2 

44 

0 

2 

43 

58 

3 

II 

S8 

23 

22 

37 

40 

4 

2 

20 

1727,  M 

nr. 

«9 
20 

21 
23 

Sept. 

5 

6 

8 

II 

1728,  F» 

•h. 

•3 

Ai 

IK- 

30 

©  Ir, 


II  48  27 

50' 

36' 

59  3' 

I 

42 

58  394 

0 

49 

— 

59 

6i 

11  48  isS 

5° 

25 

47  39 

— 

46  9 

48 

57* 

43  46* 

45 

55 

«'  52  38 

54 

52 

12  48  I2i 

50 

22 

1727,  Mar.  21.    Alt.  ©. 


8  53     8 

58     7 

o  42 

5  48 


27  20 

28  o 

28  20 

29  o 


5  37 

o  37 

58     4 

52  55 


II  59  224 


'8i 


•'   59     3ii 
■'   59  44i 


Devi. 


40  !S 


1728,  Feb.  13. 

9  47  0 

■  59  38 
1728,  Aug.  3c. 

22O  0' 

10  30  24J 

47  45 

0  57  16: 

42  5°4 

48  0  >  Uii  peu 

48  15' 

•X   gauche  i 

46  464 

centre. 

50  46 

48  3° 

0  45  52: 

The  following  table  is  given  on  the  first  page  of  volume  36,  which  contains  the  observations 
of  1732-33.  It  seems  to  be  derived  principall.v  from  observations  in  1733  not  toniid  in  the  record, 
but  this  is  not  certain.     I  give  the  table  in  the  order  in  which  it  is  found. 


y 

*                                                                                                                                                                                          '■■■■. 

174                                          RESEARCHKS  ON  THE  MOTION  OF  THE  MOON. 

I)6utii)HiMuii  (111  qiitirt  dii  circle  Itxc  i|iii  est  iIhiim  la  tuur  occiiltMituli-  Htip,  it  I'i^gard  du  la  ni<^ri- 

tlleiiiie. 

Hiiiiteiirg. 

18°                  40    sec.  al.  occ.  ) 

*'                     ^°\                       !•  Tlii'80  lirst  lour  in  a  ditt'creut  liaiulwrititiK  from  the  utkers. 

21                          4»                             i 

"'84  5°'                43. 

SS                        44 

54  54                 43 

38                       43 

33  37                   43                                                                                                                                   ■:  ;.,  -v;.;      ;.  ••./ 

»3  54                 4' 

>o  «3           4«                                                                               '.  :; .;';  • 

18               40                                                   ,•■■".' 

18                   i9k 

18          m 

,    30                   0 

If  this  table  ret't^rs  totlio  iiistninn'iit  with  which  the  sun's  transits  wen*  coinnionlv 

observcfl,  the  numbers  wonhl   s'.m'Iii  to  Ik;  ton  ^rn-at  for  use  in  previous  years.     Hut  it 

confirms  the  siispieiou  of  an  increase  in  the  error  of  the  (juathant. 

1738,  Jan.  2.     Occiiltatiiiii  of  Aldehanui. 

945     7  on  8,  c'i>ck.     Aldebaraii  eutre — piirtie  obscure               9  39  5'  app.  time. 

J  16  tub. 

II     6  24     Aldebaran  sort.                                                                11     16  app.  time. 

Jan.  I      0tr.    0     2    .(6}        5'   9"                          4  52"     Midy  A  la  peadale. 

2                 0     3     41            —                               4  S4       Mid.v  vray. 

3                 04     36          6  57                              5  46^     Midy  pend.  inf. 

'o  37 

fdtki             Til             -i-Sii         rjX                                                                                          ^.,^^^___ 

tiaii.  2       VI       )  ^^)     54a                                                  — 

I       4j                                              16  23i 

I      ■'-,■*             - 

'       ■ 

9  3°° 

Aldebaran  tr.  9  32     14           513     subtr.             16  25^     Mid,v.  pend.  sup. 

1738,  Dec.  23.     Occult,  ot  .Mdebiinin. 

5  50  35       Immersion  partitM»l)scnic,                Dec.  19      ®  tr.          0''  13'    53"          15'    15"} 

16  28J                                                                         20     ©                °     '3     27            15     49 

5  34     64     Inimersion  lieuie  vraye.                            23      ©                     '.S       74           >7     2oi 

Aldeb.     10     j8     51 

6  50  36       Hmursioii.                                                             S              10     34       0 

—  I C  30                                            ■ 

T  1         f?\                        IT        f  r        11                    1 R           1 

•4*^                  01541               10        J 

6  34     6       Kmersion  lieure  vntvc. 

A  great  gnomon  was  established  in  the  year  1729,  and  it  niav  be  that  the  transits  of  the  suD 

were  observed  over  it  after  that  dale,  lint  1  iini   by  no  nu'ans  snr'.     A  correction  of  -|-  2' i.«,  bow- 

ever,  applied  for  error  of  nu'iidisin,  and  it  seems  to  be  well  delerniined,  though  I  do  not  know  how. 

•739'  ^''''''-  '5      ''  5°  3-'     I'lini.  <if  "  Tauri                Clock  5'  i"              App.  time  6  45    31 

Feb.  13      noon  by  5  good  corresp.  altitudes        0°  4'  57".3 

16     per  guomuii,  uiieorrecle«l 04  58.7          Corrected    05     0   .a 

1 ' 

RESEARCHES  ON  THE  MOTION  OF  THt  MOON. 


175 


1755,  July  6,  ii.  111. 
4  38  S3     ImmerHioii  of  Aldelmnin.  3  telfscopt^s. 


ul.V     4 

0 

10  J3i 

1 J 

404 

("orrt'i^tidim 

to  "  . 

^iir 

,il' 

i«'r  »!orri 

s 

.S  .•i4 

7 

50* 

6 

$  434 

8 

04 

'?S5. 

•Ian, 

23 

-  6'.2 

9 

6   12 

8 

28J 

Apr. 

'5 

-o'.7 

16 

''  544 

9 

1 1 

Apr. 

21 

+  o'.3 

nl.v  if> 

Arctiirns 

6 

30     » 

.Mii.v 

5 

+  o'.6 

•7 

Arcttirus 

f, 

26   10.8 

Mil.N 

26 

+  '••5 

18 

ArctiiniK 

6 

"   '3  5 

J) 

7 

53  JS-» 

.Ill 

l.v  iS 

( 

orroNp.  altM. 

«9 

0 

7     '■' 

9 

2l4 

0 

-•  43 

3 

8  3'-S 

'755i -'"'.V  18    </'  15'  17"     Itiiiii.  «  l.il.ru- per  3  oliHorveri*. 

1757,  I'Vb.  25,  p.  III. 

6  S3  S7     Iniiin>:Hioii  of  Alili'liiiiiiii. 

8  II   29    <'.<miiii'iiwiiii'iit  lie  IViiifiNi il  fiiit  uiu'  t'ohaiuainf  iiii  IidhI  iclmrc  de  1h  lime,  et  a 

esfi'  plnsicins  sccoiidcs  saiis  hc  siii.iriT  ilt'  In  liiiid  df  lii  liiiii',  ce  qui  iioiih  a  foit 

I'toniif  ,Mr.  di^  Tliiirv  i-t  iiuij. 


II  39     II  t'st  totaU'iiit'iil  scparc. 


Fi'b.  24 

0  tr. 

0''  18' 

26"  ,, 

to' 

•3«"-5 

»S 

18 

1-' 

20 

31 

36 

'7 

57 

20 

8.7 

4  33  44     iliiiii. 

5  54  35     t^niersion 


-.1  16 


a 


-9  '7 


i7S6,  l)ev.  13. 

9   10'    29"  80  o'  3O  «'    18" 

•3  35 

16  4'''4 

io  3 

23  20 

jfi  41 

3°       »J 
1756,  Dco.  I  J,  ft.  ni. 

4  24  28  Ouipc  ) 

I  2o  50  >  Copy  winiplete  and  literal. 


8  20 

3     5 

44 

8  40 

3     ' 

54 

9     0 

5« 

4.4 

9  20 

»  SS 

184 

9  40 

-•  5* 

0 

10     0 

2  48 

41 

5  45  '*' 


Dec. 

13 

0  tr. 

0    7  58       10  21.5 

«3 

a.  HI.  KeKuliiH 

4  40  52.5 

«3 

© 

8  20          10  42. 5 

«S 

0 

9     6             - 

lb 

0 

9  30-S      "   53 

'7 

© 

9  54.5      12   16  IViil.  8"  xoiist, 
1758,  F.'l).  17 

10  36  js 

TmmcrHloti  of  ;-  (ii'iniiiornm. 

Feb 

'5 

0tr. 

0    3  144         5  28 

16 

3  524         6    (' 

«7 

I( 

8    9    OJ       10  51  (ie  viMitrc) 

r  Gem. 

8  14  594 

18 

< 

8  59     ='4 

«9 

0 

0     5  424        7  554 

Jan. 

a3 

0  20  47        23     (>i 

»♦ 

20  s»4    23  "4 

1756,  Dec.  17. 

O     ,0' 


7   '54  7 

10  20  7  40 

13  304  8  ° 

16  404  8  20 

"9  534  8  40 


Jan.  24.  1758. 
9  47  52       14     10       2  ^(>    20     lioniif>. 
51    14       14     30       2  52    S7     ""'''• 
5441        14     50       249    3i     118.S1 /.  lioniii', 
o  22     7j 
-  '3 


Did.  iiiiiial  (?) 


74 


176  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Sebieb  V. 
OhiiervatloHt  by  Dklislb  at  St.  Peterxburg. 

TIu>s(>  nbservatioiiH  have  iievor  been  |niblished.  'IMio  oriffiiml  maunsi^riptH  wei-e 
rcfainerl  by  Dki.imi.k  wboii  Iw  rctiirn(«l  to  I'jtris  about  1  749,aii(l  wen>  eveiitMally  depoH- 
itiMl  at  ibc  l^iris  ( )b.s«ivatorv.  In  1H44,  tliey  were  claiiin'i!  Jty  th«»  Uiissiaii  (Jovcrii- 
inciit,  (Iclivorod  to  Ottcj  oTkiVE,  ami  dopoHiteil  at  tlio  Piilkowa  Observatory.  A  full 
rep(»rt  upon  (Iiein  was  made  by  Stkiivk,  wIio  called  attention  totbe  poHHililo  value  of  tlie 
((bservatiouh  ot"  oceidtation.s  of  the  I'leiades  wbirh  they  eontained  Tlu'se  oecnlta- 
tions  were  discussed  by  Linshkk  in  1.S64,  who  compared  th«'  observed  times  with  those 
computed  from  IIansk.n'h  iiUmir  'l'abh>s,  showiiifr  a  in»u\  a<;r(fement. 

Desirous  of  inchidiu^-  in  the  present  iuvestitfation  all  that  was  vaiiial)l«'  in  I)k- 
msi.k's  observations,  I  took  occasion,  dnrinjj  a  visit  to  Pulkowa,  in  .Manii,  1S71,  to  ask 
Stkl've's  pormi.ssion  to  examint;  the  manuscripts,  and  make  extracts  for  the  purpose  in 
vitnv.  This  was  very  kindly  ;,'rantod,  and  the  services  of  the  secretary  of  the  estab- 
lisluncMit,  Mr.  Lisokmaw,  were  placed  at  my  disposal  whihf  en<^a<j;od  in  the  examina- 
tion of  this  and  the  other  tn'asures  of  astronomy  which  are  contained  in  the  library 
of  the  ( )liser\  atorv.  I  retain  a  very  pleasant  recollection  of  .Vfr.  liiNOKMAXs's  courtesy 
in  ronderiuff  this  assistance. 

The  extracts  from  I)bm.si,e's  manuscripts  are  fr'iven  quite  fully  in  the  followiuj? 
paj^es.  The  reduction  of  the  observations  has  ^jiven  sonu'  frouble,  owinjj  to  the  uuil- 
tiplicity  of  docks,  and  the  varyin}^  and  irref^idar  manner  in  which  the  time  and  other 
observations  were  uuule  The  j;;enenil  systtMU  of  (diservation  was  the  same  hh  that 
pursued  in  I'aris,  the  transits  of  the  sun  over  the  meritlian  of  a  gnomon  i)ein{;  observ«'d 
(piite  rei-ularh',  and  the  error  of  the  ;iiiomon  l>ein}jf  iletermimnl  frouj  tin>e  to  tinui  by 
correspondiuj^  altitutles  of  the  sun  before  and  after  n<(on. 

rianc.  of  iiltservatioii,  ()t)si>rvatuire  laiixirial  en  iSiisile  Ostrow. 

1727, 1e  21  ft'ivrier,  nouv. 


Hauteurs  iln  Holuil  |>our  I'liorloKe. 


MXin. 

37 
39 
4' 
44 


ao* 

S» 
8J 
2ii 

44 

2 


'4" 

16 

18 

20 

22 

U 
16 


UniiUMirH, 
13O  16' 
'3     46 


•3 
'4 
<4 
'4 


S6 

r> 
16 
26 


rt<>ir. 

2"  38"  3oi*' 

32        «J 

*9     43 

»7     »8J 

2.S       9 

"     S^i  3 

Ije  a6,  linutcurH  du  8ol«il  pour  I'horloge. 


Milieu 

(Correct,  tie  NuUiuti  Houst. 
Midi  vrai    ..... 


26* 
28 

58 


■7" 

'3 

'7 

>7 

•9 

•9 

21J 


13°  S6' 
14      6 


9''   aS"  2  3' 


«4 
>4 
•  4 
«4 
«4 


16 

26 

36 
46 

S6 


30 
3» 
35 
37 
39 


44 
I 

9 
'3 


'5^ 

6 

«5 

16 

«S 

26 

•S 

36 

'5 

46 

«S 

56 

Ix>  27  Wvrier. 


Le  soir  li  8'>  42"  II' (If  l:>  poriduli!  iiumersion  daus  la  partie  obscurti  de  la  lane  il'ane  forte 
petite  etoile  d(i  la  ((ueuf  •III  l>t:lier.     II  y  avait  2  auin^s  <itoile8  |ilu8  coiisidiirablus  situiu's  ainsi  .  .  • 
Lo  temps  vrai  d<>  cette  iinniersion  d6duit  des  inidis  le  21  et  28  f6vrier  est  1^  8'^  40"  53*. 


RKSEARCHES  ON  THE  MOTION  Of'  THE  MOON. 


177 


l,«^  28  (lisTicr. 


naiitfiii'H  (III  koIimI  pour  I'liorlogt . 


9"  9" 


Muiiii. 
29" 


1 1 
'3 

'5 
'7 
'9 
21 

23 

^5 
27 


26 
«3 

'9 
16 

1 1 

12 

30 

»7 
314 


lluiitciirH. 
140  16' 
14      2(1 


14 
I  t 
'4 
•5 
15 
'5 
'S 


36 

.,r. 

5''' 
6 

16 

.■r, 
36 


29  27 


IS  46 
'5  56 


i*»  Mtiir. 
2"  S3'"  46' 

5'  484 
49  S«4 

47  S'' 

46    o 

44   S 
42   o 

39  534 

37  47 

35  43 

33  464 


MiliiMi. 
•■"  374 


,1 


llaiitiMir  in^ti'iil.  tin  boni  Niip.  ilii  sole 


o" 

°  '  37i 

o  '  37i 

o  •  374 

o  1  38 

o  1  36 

o  I  36 

o  I  3051 

°  '  37 

°  «  37i 

°  «  37 

22^  17'     15"  fort  CXrtftt' 


MiliiMi  sikim  corrt'ctioii    .    .     o'' 
<  j)i'i'cciii)ii  ilo  Niuliits  soimt. 

Midi  \  rai o 

Midi  vrui  1(?  21 o 

Difft-rt'iice  pour  7  joiirn 


I'" 

37" 

- 

28 

I 

9 

2 

58 

I 

49 

3 


Iiisteatl  nt"  ilcpiMuliiif;  on  tliR  i'lo»rk-rato  tVom  tlic  alrirndcs  of  l'Vl»niai'v  21  iiuii 
Ft^liriiary  2S,  I  Imvi!  iitili/cil  those  iiijuio  on  die  inoriiintr  of  tim  26tli.  By  ronipntinj^ 
till'  iiltitiidr  tVoiii  the  cuiTcspoiKliiij;-  oljscrviitioiis  ol'  Kchniarv  21  and  2S,  it  appoars 
tliat  tlic  allitiidi's  as  ;jivcii  rciiniro  m  corivction  oi"  — 16'. 2  tor  seini-diaint'tcr  and  index- 
error.  Applyin}"'  this,  we  liave  an  error  of  tdock  011  apparent  time  oi"  i'"  4i'.5.  We 
then  find:-— 

Clock  F.-isl.     K'luaiion  of       Cluck-cor- 
I  App  Time.  Time.  rcclion. 


./      » 

w 

/ 

Fel. 

35. »'  ■» 

1 

41.5 

38,   0.0 

' 

8.0 

+    13     35-3  .   +    I'     43-8 
+    13       0.4  j    4-    II      52.4 


Fntorpohitini;  to  the  time  of  the  occnltation,  we  find  : — 
Chick-time  of  oeciiltation  of  rr 'I'aiiri,  1727,  Fehrnary  27       .     .     8''  42'"  12'. 

Ch)ek-correction ii"'4g*.8 

Local  mean  time S""  54"'     r'.S 

Greenwirh  mean  time 6^  ^2'"  ^K.t,  ±2'. 

(kciiltatiiiiis  of  the  Pleiades,  1729,  Deamher  3. — Tlicsf  oh.->frvatioiis  licinjr  jriveii, 
in  extetiso,  by  Linhskk,  in  the  |»aper  already  refernMJ  to,  I  math'  no  copv  of  them,  bur 
only  eompared  the  orijiiiml  here  and  there  witli  Linsskk's  printed  data.  I-  M'ems 
.siirtifient  to  present  those  of  the  results  most  likely  to  jiive  ri.se  to  cpiestioiis.  Lin.smeu 
}(ivos  the  followinjf  resiilt.s  for  correction  of  the  time  of  sun's  transit  over  t!ie  gno- 
mon.-— 

1729,  Nov.  23 -f  l"S 

1730,  Feb.     I -f  3'.8 

1730,  Mar.    4 4-8'.2. 

But  ho  makes  no  statement  of  the  corr(>ctioii  wiiich  he  actually  iidopls,  nor  of  his 
<,'roiind8  for  ailoptiny;  it,  only  remnrkin^f  that  it  is  interpolated  from  the  above  v.iliics 
By  calculatinjf  backward  from  his  results  for  clock-error,  imd  his  tabular  data,  he 
would  seem  to  have  adopted  -|-i*.o.  It  would,  therefore,  seem  that  he  coiisiriered  the 
;ja— 76  AP.  2 


17S 


RI.SF.ARCHKS  UN   TlIK   MOIIDN   Ol'    IHK  MOON. 


t'orrectioii  to  varv  witli  tlic  ilccliiiiitinii  ><{'  tlic  .>«iin  nitlicr  tlmii  with  the  thiu'.  Hut 
whoii  tlie  results  for  several  veins  iH"  plaeeil  tojiether,  they  a|)|»ear  to  van  only  with 
the  time.  1  therefore  ailojited  +2".5  for  the  correction.  'I'lu'  addition  of  a  slight 
dirterence  in  the  ('([nation  of  time,  arisin;--  iVom  the  |ieriodic  |iertinl»ations  of  the  sun's 
longitude,  Iieing  neglecte(l  in  my  work,  carries  the  ditVerence  of  computed  mean 
times  up  to  2",  an  amount  l>v  whicli  my  mean  times  are  less  than  those  of  I.inhski!. 
The  following  are  mv  independent  results,  alongside  of  which  I  place  for  comparison 
those  of  Ll.N'ssKK.  The  results  are  a  mean  of  thos(t  from  the  two  (docks  (J  lUul  D, 
which  diti'er  between  themselves  hy  an  auioimt  varying  fnun  r.4  to  l".o. 

/Mli;  I7ay,  Otifiiiher  3. 


«i" 


Sl;ir. 

Local  Mean 

Tinir  ol 
(>;  iillation. 

l.inSMT 

Siduifal 
Tiimv 

(irt'uiiwirh    i 
.Mean  'I'iinc.  1 

// 

»t 

T 

s 

1 

:   A   m 

' 

km       1 

Uleclia 

1(1 

35 

??.') 

i')  ' 

n  27 

24.  <) 

14  34    444 

Ccl'.una 

41 

yy(. 

41? 

33 

7.(. 

40  2(1 . 1 

Maja 

17 

Id 

■;...(i 

58. S 

lo     « 

30  3 

1 5   1543' 

Mfiop'' 

Jl 

4-4 

4<).7 

23 

23.'i 

3"  33. y 

Alcyone 

43 

13  f 

■5  '■ 

.1'» 

52.7 

47     0.3 

Pleione 

l» 

J  2 

"7  4 

I'l  7 

II    .4 

3-5 

If)  31     3  g 

Alias   . 

37 

3i.'- 

37.7 

M    29 

22.6 

3ft   22.1 

1733,  Ic  2  2  Mars. 

A  iiiiili  vrai <I 

I) 

N 

M 

lift  miir, orcnltiilion  v  (|ui  est  dans  iiii  (Its  picds  dcs  Juiiiciiux.     liiuiicrHion  tms  t-xaclc  i\  7''  24"' 
I't'udiili'  N  iivcc  pliisicurs  liuu'ttbs.     I'^iiioisiDii  a  8''  jo'"  20'  i  tr^s  iiKUTtaiiu*. 

( '<iiii|iaiais<iM  di'M  jiciidiilcs. 


11"  55'   17" 

II  219 

"  57    .s<; 

"  .S4     "7 


7''  24 


liiiliiiMliatciiiclit  apies  riiiiiiiuisioii. 

51^'         6''  31'"  o' 

7     25      S'4  '•     S-     " 

f  l> 

li'iiniiKM'sioii  est  (loMC  iirrivi'c. 

Anx  iii'iiilillt'^'.  All  leiiiim  \  iiiIm. 

(J 
l> 

N 


27'"  4i.i" 

«"  3<'"  57" 

7 

2«      4  <  h 
N 

C 

liiiiiicdiiitt'iiKMit  ii|ir6s  I'cmerHiiMi. 

7''  38"'  o*         8''  34™  49" 


f   I,il   IXMldlllc  K  (\  CI 


INuifc  (■'((•  lUT«'t«?(', 


u»  54""  47» 

'o     58     59 

003 

"      52     i^ 


II  5.5  275 

'o  55  48 

«•  54  3'4 

««  53  7 


RESEARCHKS   ON  TIIF,  MOTION   OF  THE  MOON 


179 


Ia'  25  Mars. 

A  iiiiili  vriii (' 

1) 
N 
M 


"54       5 
10     52     3? 

"      54     4' 
I  I      JO      29 

Le  8»ir,  occnltatiiui  ilc  «  5  ilaiiN  iiii  instant  i\  7''  15'"  i^'i  <••"  I"  pfiKlnlt'  •'• 

(•  N  i> 


AjUf's 

riiiiiiifrNion 

L'iniinHiHicin  est  ariivi-c. 

Aiix  |>i>n<hilt'ii. 

C 

7"    >5"'  444" 

I) 

6     ..',      ,84 

N 

7      '^'     i<) 

7''  irt""  o' 


7"    '«  44i" 


6''    n)"<   o" 


i  \i>{  pi-mhilc  .M  11  fic  n-tardct'  27"  on  la  rci-on 
[■      tant  ct  avani'i'-c  10  niiii.  pour  l'a|i[)roclier  ilii 


I  A'  27  .Mar.«*  a  luitl.v 


It'inps  villi. 


39 

37^ 
38 


I  Mil 


leu 


i  Corrrfliiin 


r<inl.  K      ....     I!     49      8    32 
Diir.  iit-ntl. 


All  ti'iiipH  vriiiH. 
7"    2  1'"  47r 
7      i'      47 
7      -•'     4« 

.1'     53"    .2* 

1  o     4^1        1 
>>      54     4-' 
o       o     424 

I)an«  ci'N  laltMiN  dii  iiMups  vrai  il  ii',\  avail  point  (IVnciir  ;\  la  int-iitliennt'. 
(To  ilt'torniiiu'  tho  ifvnn  ol  nu'iidian.) 

Lc  io  Mars.     HanttMir>  >lii  lioid  siipci  i.'iir  tin  solcil. 

IVnil.  Iv  H''  2,\"'  If     iS"  2>'     3"  i.S'"  <'7"       ""  49'"  M\'1 
"        °  14     20 

;  •     42 
I  I        I 
9     21 

7     43 
6       4 

4       ■!•! 

-      44 
I        6 

.?9     ^S 

57     40 

I.C  2S  Mais. 
UncorrtHJtt'il  tiiin-  ol  appart'iil  noon  fioin  (loiiUli-  altitinK-.-s  witli  -lockt' 

Correal  ion  of  KnU-r        .     .    .    > 

True  noon  pi-r  clock  C    .     .     .         • 

Hirtfii'iict' 111  (locks  at  noon  1 19  —  ♦') ,    .    .     .     . 

Iruc  noon  l>v  dork  I) ■ 

Traimit  ol  snii  per  rliMik  1> 

Coi«r»'«!lioii ,     ,     , 

Tlic  results  for  convctinii  of  friioiitoii  an-  — 

1733,  Marrli  20 


24 

5« 

iS 

3> 

26 

3'> 

r.S 

4" 

2« 

"4 

i.S 

5' 

^9 

55 

'9 

1 

3' 

32A 

'9 

1  1 

33 

1 1 

i<) 

21 

34 

534 

■9 

S> 

3(> 

3« 

'9 

4< 

3« 

1  2 

'9 

5' 

39 

5' 

20 

I 

4' 

^x 

20 

1  1 

l''  49'  38"  11 '" 

-'9    39 


3 


•'^l  ;.  I'.iiiliilf  I) 

37.'! 
37» 

38 

18 


o  40  30  30 
n  8  38  2 
II        8     39    22 


('orretftion  ilc  la  inc 
riilioniu-     .     .     . 


3 


ii''     53'"  '4"  7 

—  29.  () 

«'      5*  45-  ' 

I       9  57.  o 

10     42  48.  1 

10     4)  4».  7 

—  0.0 


-l\S 

Mari-h  tK        —o'.h. 

riif  vaJiK   —  I'.o  1ms   i»i'i*i»  a«lof«r<l.     Tli*'  (•♦trPwtMUis  «4  lh»-  fhri'e  cliuks,  (",  I>, 
ami  N,  w*»  tht»i»  found  to  \tv  as-  fol!o»»:- 


At  ii])]Mir<.Mit  lUMiu, 


1 1"  5IP.5 
I  ;■  3".o 
12"  i8*.4 


I) 


■fb4'"  45V> 
07"  46'.  3 

73""  36'.o 

70"'  2y'4 

82"  2  2*.  5 


-i-Q'"  5*-.V 

b"'  4 2'.  5 

I  !'"  2  7".0 

10'"  4  8*.  4 


IcSo  RtCSEARCHES  ON  THE  MOTION  OF  THE  MOON.  ., 

\Ve  tliiMi  liavo  the  foll.nving  results  for  moan  time  from  the  three  clocks: — 

1733,  March  22. 

IiiiriitM-sioiis  of  I'  ({cMiiii   dock     7''  21'"  i8*.5         6''  27"'  27'.o         7''  24"  8'.5 
( lock-correct  ions     ....        -f-  i  i'"  5o".7  i''     5*"  41*4  I 

Mean  lime.s y^'jT'    9".2  7^' 33'"    8'.4.  .     . 

1733,  March  25. 

Immersion  of  'c  Oancri,  clock    7''  i5"'44".5         6^  13"  i8".5         7''  16"  29'.o 

_l_    ,2-1.     j;.^  ,h  ,^M,  ^Q,2  ,,,„  2,, 2 

7''  27'"  49".8         7"  27"'  48".7         7"  27'"  5o".a. 

The  mean  of  the  limes  jriven  by  the  several  clocks  will  be  adopted, 

■yj**! 'Vpril  14.    Tiaiisit  of  sun's  centre,  ciock  A,  i' 3j'»  iij*. 
l!oin|iiiiisou  (if  clock.s \I         ,(.  ,gin    q» 

A         ■     35     '7 
N         1     5a    43 

liinni'isioii  of  Aldebunui  instuntiineous  at  M,  11'' 56'"  30'. 

ArttTwanl ;yi       ,,ii  .gm    q» 

A       II     55      5 
N  o     13    »4j 

"  LVrrenr  <li>  lii  moi'iilienne  est  (i'envirnn  7"  addftive." 

Times  (if  the  innnersiuM. 

I'en<lul«!ii.  IViiiiM  vnii. 

A         ii''    S3'"    35«  ,0"    19-    5j^' 

M         II      56      50  ,0      19      ssi 

>J  o      I'       S4i  10      19      3«ij 

April  13.       rtnn  on  meridian A        i''    jc"  J58* 

M        '     38    37i 
^'         '      54     S4i 

Applying  +b'.^  for  error  of  ;.iUoiuoM,  we  have  tlie   following  results  for  elocl  - 
correction: —  . 

A  *  M  N 

April  14     Apparent  noon  —92'"  10". 7         —94'"  5 3". 7         — I09"'36".7 

15.    Apparent  noon  —  95'"  40".o         _98'"5i".7         —115'"    S".7. 

The  mean  time  of  the  oliserved  occiiltation  is  then  found  from  each  of  the  clocks 
as  follows: — 

1736,  Aj.ril  14. 

A                             M  K 

Clock-times  of  inmi.  of  n-Tauri    1 1''  53'"  35".         r  i''  56'"  3c".  12''  i  i'"  54'.5 

('lork-ci.rrecfions  .     .     .     .       —  i'"  33'"  4o".7  — 1''^0"' 36".!  —i^^i<»^g\j 

luteal  mean  times        ...         10    ig™  54".3        10''  19'"  53*.9  10''  ic)'"  54'.8. 


RESEARCHKS  ON  THE  MOTION  OF  THE  MOON. 


i8i 


1736,  June  20,  • 

TliP  i!orru(!tioii  of  tlm  iiii^riiliuii  if)  foun<l  to  bo  very  ii<:curiit»«l.v  +  'j.i',  U>  Im  hiIiIimI  to  the 


ol>M>rv('il  tinieH  ol  triiiiHit  of  the  huh. 
AuK>  ■•       TriinNit  of  the  huh 


I'eiiilulf  iiouvflle,  iifterwanl  Hto|)|>cd 


A       8"  45-  34* 
M        8    41     58 

[8     48     40]  uouvclle. 
8    48     22   HU|i(3ri«Mirf. 
59"*     9i" 
'o     59 


A 
A 


2'' 
4 


Next  iiioniiiig  iniiiifrsion  of  Alditltartiii  very  exact     .     . 

eitifrHJon 

".le  orois  iiu'i'lli'  lie  fiiiMnii,  ijue  ile  Hortir  <|iiaii<l  Je  I'ai  a|ier\Mi  oar  jY-taiH  fort  attentif  el  elle  iii'a 
imi'ii  iralionl  fori  lirillaiil  a  IViiilroit  tie  la  luue  ou.i<<  ratteuilaJH." 


AprcH  riiiiiiierMioii 


M 
A 

8u|i. 


2''  58"'  o* 
3  '  4oi 
^       4        2'> 


Apritit  I'eiiierMioii 


liiiiiierHioM. 


M 

A 

Sup. 

Kinei'HioM, 


4''     0"' 

4        12 


39 

26 


A 

M 

Hup. 
Aug.  2. 


2 
3 


Clock. 

59'"     94" 
55     29 
'      55 


(6' 


True. 
'    10" 


34*1 
6  10  25I 
6     10     27^ 


CliM'k. 
4*"   10™  59' 
4       7      20 
4     "3     46 


8uii  uii  iiierliliaii clock 


A 

M 

Sup. 


Truf. 

(7''  2  2'"  56*] 

7  22  47 

7  22  484 
8''  49'"  2  2* 

«  45  5° 

8  55  '5 


1  Hiid  110  reiiaon  given  for  rejecting  clock  A,  ex(!ept  its  (liHconlaiue. 


I'rocecdiiitj:  us  usual,  and  adding  +  9".2  fnr  error  of  giininoii,  wo  liavo  the  fol- 
lowing resnltfj  for  «!oiTection  of  the  three  elocks,  A,  M,  and  Sup: — 


M. 


H""  45'"  43'-2         S''  42"     ;'.2 


Sup. 
48""     .3  I '.2 


15"    20' 


5"'  46*.9 
■     3"-7 


8"  49'"  3 1*. 2 


,5-  23'"  39".; 
8"  45'"   59"  2 


>5" 
8" 


>7" 
52' 


o*  .')•" 
5"  16"' 
2"  50" 


42".9 
•••.7 

9"  5 
is"   1 7"'     8'.o 


2'' 

•5" 

1 8" 

4" 
•5" 


I' 


(/lock-times  t»f  traiiKit,  AugiiHt  1 

Mean  tiin*' 

Clock-forrections 

Clock-tiniert  of  t<:iiiHit,  .Vngnst  2 

MoiUi  tine      .      ,.♦».. 

(Jliwk-»"»>rrection» 

Imni«*si(vns  .»f  a  'raiiri,  clock  . 

( 'hMik-«'o«Te*tioiis     ..    ,     .     »     . 

MewB  Utm>» I H''    1 6'"    )  7'  5 

Ljn«isi.>TiH.  ch>rk 4''    to'"   $</ 

( ;iock-ootTe<ti«nis     .     .    •.     .     .     .      15"    !  6™    56".4 

Mean  tim.-     .,*.....      19'  27'"  55',4 

In  tk)ubt  wl*rtlier  to  mpvt  m  mtatn  i  lock  A.  I  Hhnli  gi''"  it  half-weight  in  taking 

^le  tneaii. 

< Mil    .itian  (4  AldelMrtiii  Oct.  23,  a.  in.,  1736. 

1     n.i-^     I  v(^- (•sact  »i  hrigfcr  ItiU         .../,....        A        ♦*  .$^"  58* 

I'.lllclrtliKl ........  A  f/        6  I 

"...  (juoiqu'il  .V  "Ul  UII  grHiiil  luiiuilliiril  an  traverw  <lei|uel  li*  lune  pHi<4tiMiii-i  et  qui 
einpii'liail  ilc  liien  (ll<*tlngner  les  ti'c!ie,s  ;  cept'iitlant  a.vaiit  encore  ilirigc  la  lunette  eatailioptiiqiu-  i^ 
I'emlroit  on  se  ilevait  faire  eett*'  iMiiermoii  j'ai  coinaiencc  a  voir  Alilebaran  sorti  ile  deasous  la  luiie 
a  6''  6'"  1"  tie  U  peiulu'e  A  etje  c  ois  que  ce  temp-*  C'il  le  premier  moment  ile  son  emersion  u'ayant 
rien  vti  (hju  do  Mocoiids  uuparavaut  uu  meiiie  endruit. 


15''   i9'"  43"7       '5''    KV 

55"  29'.o 

20*  40*.9 

1 6"'  9'.9 
7"   20'. 

20"  29'.  2 
1 9*   27'"  49".  2 


'5'7 
24'.  2 

18'.  7 

55"-o 
15"  14'"  1 6'. 2 
iH''  16"  Il".2 
4"  13'"  46*. 
15"  14'"  4*-4 
19''   27'"  5o'.4 


l82 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON 


"Oette  occultatioii,  Htiivatit  inoii  obHervatioii  t'xt  iIoik;  urrivtio: — 


L'6iiu>rMioii. 


IN'iidiilt'N. 
6''  6"'  1" 
6     ..      6.^ 


L'iiiuiu'i'HJoii. 
I'uiiiliili'N.  IViiipit  \riki. 

A  4''   50"'   58"  3''  o"'  32* 

M  4     47        6A  30     36 

The  (iatii  for  clmik-error  lire  Hoiiitnvliiit  irrt>i;iilai'. 
We  have: — 
16  octobre        Hiiii  011    iiioriilian  (({iioinoii)       A 
TraiiHit  of  sun  over  5tli  wire  of  mural  sext. 
I'aHsajjo  of  diameter  2'"  loj* 

Peiiihile  A  eiisnitc  arnttee,  et  la  peiuiiile  M  a>'  .iieee  7  mlii. 
AfterwanI,  tlie  followiiit;  transits  over  5tli  wire  of  the  luiiral  i|iia(lr.iiit 


iiiiiilM  vriti. 
4     «5     jC'' 


1  r*" 
'9 


JO" 

ni 


M 


,ii  ,«i.,  J  J. 


Oct  18. 

20. 


Hiiirs  II  limb  . 

f  A(|uliae      .  . 

a.  Aquilae     .  . 

/S  Aqiiilue    .  . 

Mars    .     .     .  . 

i^yk     .... 

Bor.  Cauil.  Ceti 
Liicida  T  .  . 
i»  Hyad.  .  . 
([  bord  siiivaiit 
Aldubaraii  .  . 
Kigel  .  .  .  . 
Hollatrix       .     . 


Halt.  Orion. 


At 


23.       rtun  II  Had)  i 

I  llera  DEi.ihLB  ' '  Bit;>iM)Ht'ii  ri  I  III  uf  nierliltaii      i  W\  ^^\:\  oiiiU.  f 

^  Aquihe 7 

.Inpiter 8 

Nodi  X o 

.Mars I 

La  pendnle  M  a  ('le  ain-ti^e.     Pendule  A,  Oet, 

Nov.  4.       Hum's  centre  (mean  of  limbs)      .    . 

(iiiomon 


34' 
32 
3''> 
4' 

'5 

37 

5° 

3 

iK 

>9 
r 

'7 

21 
26 

•  3 

,v3 

4' 
42 
.S3 

o 


'  4>!i' 
44 

59 
2«i 

.S' 

.s° 

3°^ 
3-»i 
28i 

■■i 

54 
3S    j 

36M 


25 
ret 


M  =  A  -  1 


— ,;"'  52"  at 


4"  54" 


\ 


M  -  A  =  -  3" 

—  4 


ssH' 

9 


Ditr 


[4'  en  la  remontant. 
A      .    2  3«  44.i 
-•  3«  30 


+  iii  (sie) 


Till'  itDiTfftioii  ti>  the  tiinc  ot'  transit  over  the  nuiriil  sextant  lor  tlu'  (Iccliwatioii 
id'  tlie  sun  at  thi«  tini*'  socnis  to  l»t'  altout  +  5'-  ^^  «'  Imve  then  tliii  following  roMiilts 
for  correction  of  clo'.'k  \: — 

I  736,  October  1 8         'iVansit  of  © —ih^^"" 

22.  Transit  of  {{ij^cl —2''     6'" 

23.  Tran.sitofO —2''      7"'  34".5. 


'.■»  -.1 


7".  2 


RESEARCHES  ON  TIIE  MOTION  Ul-  Till:  MOON. 


'«3 


luteiitolatiii},''  to  the  time  of  occultntioii  of  Alil(l)artiii,  we  liavt' : —  ► 

(Jlock- times 1 6''  50'"  58"  iS"     6'"      I*. 

Cork-i-oiTcctioiis -    2"     r,"'     5',6         -    j''     6'"   1 7".6 

Mean  tiiiK's 14"  44'"   52"4  i  j"   59'"  43"-4- 

TlicHe  results  arc  10"  less  than  those  of  Dkijsi.k,  and  more  iiiicertain  than  usual. 


For  cniii' III  iiiciitliaii  (^kikiiiioii),  April  22,  1737. 
TruiiHit  of  SUM  over  stli  wire,  iiiaral  HfMaiit    .     .     A  1''  57'"  46S"    (^'  =  A  4- 


Mvritliaii  ((;>>'**>>'>■>) 


S«      Mi 


8"'  30l" 
j''    6     444    =  (J 


Corrt'ciiiiii  of  si-xtaiit 278 

Kroiu  13  pairs  t-ipiiil  altitudes  with  clock  H,  at  a  namii  intiTval  ol  5''  42" 


Hull  at  Kicati-st  luM^lit  . 
Kuler's  correction  .  . 
True  transit  of  sun     .     . 

(,"  —  11 

True  tiaiisit  per  (! 
Oliserveil  with  ^{iioinoii 
Correction  of  k"*""*'*'     ■ 
Correction  of  sextant 


14''     7'"  37.2*     II 
22.1 


>4 

•4 
i4 


6 
+ 


•S' 

21.7 

.S3-4 

44.4 

9.0 

36.6 


'737.  ^'"i   '• 

Transit  of  sun,  mural  sextant A 

.Meridian,  k''**'"*"' 

(i.  — a 

From  12  e(|ual  altitudes  ot  the  sun,  interval  6''  56". 


2''  33'"     i'i'    C  =  A  4- 
2     3i     3Si 


'"  34     i(>i 


:C 


Mean  for  nieiidian  .  . 
Uitr.  of  clo(;ks  ('  and  II  . 
Apparent  noon  jier  (' 
Kuler's  eorrertion  .  . 
('<>rre(;ted  apparent  noon 
Error  of  ^iH)nion 
Hrroi  of  sextant    .     .    . 


+  3°* 

14''  38"'  23.8"     II 

"2      3  >9-3 
«     35       4'.S 

—  20.7 

»     34  43-8 

4-  7-° 

+  37-S 


1737.  •'^l".^  7.  s»»ir. 
Imiiiersion  of  ;  Leuiiis  (pie<l  Itorenl)  instantanemis       ......     N 

For  (jlock  ccurection  : 

Sun  on  meridian  (gnomon)  May  7 C 

Mural  sextant 

Correct.  ((!.— 8.) 

Times  of  >tn<>"«)nie  noon  lt,\  the  various  clocks. 


57'"   »7' 


2''   58'"      2'.3 


A 


2"  53"^  48.1' 

+  3-'-!' 
The  immersion  was  at — 

CJDcliH  TllW   tillU'l-. 


.V 

2'' 

54"' 

2>.,V 

(J 

2 

58 

-'•3 

M 

2 

5' 

5-3   > 

II 

■4 

43 

5 ''3 

N 

3 

10 

M3   \ 

After  which  C  wi.s  retarded 
14'  liy  windint;. 


A 

0''  41'"     5* 

'»"  45"' 

'5f 

«! 

0     44     45 

9    45 

'4 

M 

0     37     47 

0    45 

<ri 

II 

0     .30     25 

'1     4.1 

'5t 

N 

0     57     27 

y    45 

>8^ 

1 84 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


" 

TnuiHiiiitN  with  iniini 

1  Hexttiiit. 

Miiy  7. 

8ii'itm 

A 

(yl> 

30'"  50* 
22      17 

I'rocyoii 

7 

»  I     .    . 

9 
9 

S  34 
SO     S»A 

Cor.  a    . 

Cautlii  il 

1 1 

3J       S 

• 

Hpica  .     . 

1 

8     28^ 

ArcturiiH 

I 

59     58 

I'lMiiliile  11  U«;niiiKt!«l  3 

or  3  HecoiuU  Ity  tliti  conU. 

▲ 

6" 

25"'     o» 

0 

6 

28     32 

M 

6 

a«     434 

Miiy  8. 

8uii  oil  t;iioiiioii       A 

2 

57     49-7 

C 

3 

1     46.2 

M 

a 

54     24.7 

• 

H 

•4 

47       3-7 

N 

3 

14     40.2 

The  scxdiiit  33*.5  sooiitT, 


Applying  +  8".5  tor  cornH-tion  <»f'  giioinoii,  and  taking  t'roni  cluck  (,'  on  May  7  the 
14*  by  which  it  wiisi  rtitardod  in  winding,  we  Imve  tlic  lolhiwing  resiihs  tor  chick- 
correction  : — 

At  traiinit  of  ©. 
Miiy  7.  May  8. 


Clock  A 

—   2"  58'"  i7".9 

-   3"     !"•  50*4 

C 

-   3"     i"'44'.9 

-   3"    5"'46'.9 

M 

-   2"  55"'     l".9 

-   2"  58'"  2  5'.4 

H 

-«4''47"'47'-9 

-14"  51'"    4"4 

N 

—    3"  14"'  20'.9 

-  3"  i8"'40'.9 

The  mean  time  of  the  occnltation,  as  given  by  the  several  clocks,  is  then  as  fol- 
lows ;— 


A 
0 
M 

H 

N 


9"  4'" 


2 1 '.4 
19'.! 

2  2".4 

n'-3- 

20'.4 


Mean 


9*    41"  20».8 

'737t  ^^'*.v  20. 

Ten  correspondiiiff  pairs  of  sun'.t  altitudes  {five  for  thu  correction  of  the  gnomon  -f-  n'.j. 
23,  a.  III.    Occiiltatioij  of  Jupitor  in  daylight, 
•'npiter  mo  paraissait  toucher  le  bord  ccIairC'  de  la  June. 

True  tiluflS. 
le^    I"    yi" 

>  Jupiter  me  ot^raiHse  tout  entri^. 


May 

■9" 

58- 

254' 

.1 

10 

0 

•54 

H 

8 

1 

'94 

A 

8 

3 

22i 

0 

7 

59 

38* 

N 

8 

3 

S'i 

M 

16 

I 

94 

16 

I 

9 

16 

0 

584] 

16 

I 

83  i 

RESEARI'HES  ON  THE  MOTION  OF  THE  MOON.  185 

ClockH. 
liny  at.    Siui  on  Kiinrnon A         5''  jS™  Jo-S* 

II        J     56    37'S 
M        ^     SS     43-8 

Mnml  wxtiint A  3  57    41,0 

O.-S 30-S 

Mny  23     Miiial  sextant A  4''  i™  36.5" 

C  4  J    p.s  (' 

M  4  3    41.0 

H  3     59    »i-S 

N  3     5«     52-5 
Le  fll  <lo  111  iiK'-iitlieuno  6taiit  roinpu  I'on   n'li  \m  olisprvor  k<  i)iw»aKo  ilc  l'iuiUK«  J"  soleil  ik 
cottc  iii6ri(liuiinu. 

TranHitH  with  Miinil  Hcxtuiit. 
May  2>.       Venus  <      .•'"   22"    A  A        1''  i;4"'   o' 

Spica  13     3*  *'  '       5      °i 

Arctiiius  :      s       I  M         I     55      9 

Pelisj.k's  reduction  is  corrt'ct  for  dock  II.     Takiiif,'  tin-   menu  of  liis   results,  the 
apparent  and  niciui  times  of  contact  of  linihH  of  Jupiter  ami  the  moon  will  he: — 

First  contact,  apparent  time         15"  59'"  i9"-«   (o(i.i=-3"'  47'-3)  >"■  *■  =  'o"  55"  3>'-8 

SocoikI  contact,  apparent  time     16''     i'"     9".! is*"  57'"  2l'.8 

Whence  local  niean  time  for  centre  of  Jupiter    .,...,...         iS*"  S^""  26*8 

1737,  July  23,  u.  III.    Occultiition  of  tf  TiHiri. 

01(H.  llRiNMirs.  Pkuslk  flniU  : 

Immersion  of  Star  a  (men.i.Moiinle)(i.i«-!.)      A    9"  5'"  .V*^'         II  (')-'■"  5'"  ^4'  12"  sr  36'.o 
Kinereioii  of  ft  northerumost,  ami                    A     9  38      h            H        21   37     S3         ^3    3°       °- ^ 
a                                                      A     9  50     46             II         :i   50     31  13     42      36.6 

Forelocks. 
July  ai.    Suti  culii     mean  of  10  pair  cKiresp.  altitiules        8''   i'"  28.7'    II         Interval  S''  o"'. 

Enler's  conrcitiou + '3-8 

l.ue  upp.  iHion 82     42.5 

Clocks  B  —  H 9     "'O 

True  noon  B. 7  53    *o-5 

»,,  Suu  on  gnomon,  meridian 7  S3     '^-o     " 

Correction  of  gnomon +8.5 

(  Transit  over  5tli  will- oi' mural  sextant 8''    i'"  33^"    a 

norrectioii  (G.  —  8.) +  425 

Jnlv  .TV    Sun  on  gnomon       7"  43'"  5°i'  '^  ««■  ^  ('^  ''«'  "*">**  '^ 

Sextant 8  9      4      A  =         ,      jV  9'  " 

Jul>  -,.    10  pair  efpiftl  altitudes,  in'.erviil   7"  59"'    give  8''  15"' 44«.7  U 

Euler'M  correction '5-5 

'                App.  noon       8  16      0.2 

-•            Dili',  clocks,  B  —  II o  41     18.8 

App.  noon  clock  B       7  34     4' -4    1* 

Meridian  (gnomon)  B       7  34    34-2 

Correction  of  gnomon +7-2 

24 75  AP.  2 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


7 


A 


O 


A 


:/. 


Ma 


LO 

U 
1.25 


■  50  "^  ^ 

■^    aits 


1^ 


■2.5 

ii 

20 

1.8 


1.4    IIIIII.6 


V] 


<? 


/i 


7: 


c^j 


'^^  > 


^fj^^'s 


y 


>^ 


Photographic 

Sciences 

Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(71  (»)  872-4503 


i 


1 86 


RESEARCHES  ON  THE  MOTION  OF  THE  MOOI^. 
Clochcomparisom. 


July  21 

,  noon. 

22  soir. 

22  soir. 

23  a 

.  m. 

23  noon. 

i     m 

/ 

A 

m 

t 

A 

m 

t 

A 

m 

s 

A 

ni 

s 

8   5 

0 

A 

2 

7 

0    A 

50 

0 

A 

9 

53 

0     A 

8 

13 

0  A 

7  55 

56 

B 

I 

47 

25i  B 

19 

49 

47f 

H 

21 

52 

46  H 

7 

47 

5  B 

3   6 
[o   3 
II  49 
8   3 
8   5 
8   4 
8   5 

53i 

45i 

31 

30 

18 

53 

25 

C 
D] 
E 
G 

H 
M 

N 

2 
6 

5 
2 

z 

10 
0 

30 
3 
7 

46  C 
56   D 

54i  E 
57i  G 

4ii  M 

50 

II 

N 

9 

53 

loi  N 

8 
0 
ti 

>7 

4 

24 

33  C 

48J  D 
30  E 

52 
30 
56 

0 

22i 
7i 

A 
B 
C 

9 

9 

[10 

9 

56 

39 
0 
56 

0  A 

39  B 
I5i  C]* 
54  M 

8 
8 
8 

14 
10 

14 

0  A 
2  G 

27*  J 

II 

54 
47 

0 

I5i 

A 
D 

9 

58 

0  A 

II 

»3 

57 

E 

I 

51 

I  D 

8 

20 

59i  K 

54 

51 

M 

I 

16 

3ii  E 

8 

15 

4  M 

56 

0 

A 

9 

59 

0  A 

8 

16 

0  A 

52 

40 

G 

9 

59 

«3  J 

3 

>5 

55  H 

56 

10 

J 

9 

55 

33i  G 

8 

16 

8  N 

II 

56 

3ii 

K 

*  Afterward  retarded  13*  in  winding. 

The  clock-corrections  have  to  be  interijolated  from  the  noons  of  July  21  and 
July  23.  The  system  of  proceeding  will  be  this: — Taking  clock  A  as  a  standard,  we 
shall  find  the  eiTors  of  the  other  clocks  for  the  comparisons  nearest  the  occultations, 
on  the  supposition  that  A  is  correct.  The  mean  deviation  being  supposed  to  arise 
from  changes  in  the  rate  of  A,  the  latter  will  be  corrected,  so  that  the  result  shall  be 
that  given  by  the  mean  of  all  the  clocks.     We  have,  first: — 


•2 
0 

u 

B 
C 
E 
G 
H 
M 
N 

Other  Clocks,  miniit  A,  etc. 

(0 

(2) 

9°  SO"  A. 

July  21.0,  8"  s™  A 

July  23.0,  8''  14™  A 

Comp. 

Obs, 

A 

Comp. 

Obs. 

A 

m        s 

—  9   4.0 

+   '  53-5 
+  224  31.0 

—  I  30.0 
+   0  18.0 

—  0   7.0 
+   0  25.0 

m        s 

-  25  55.3 

+   4  38.0 
+  191  30.0 

-  3  58.0 

-  0   5.0 
+   I   4-0 
+   0   8.0 

Pt       s 
-  21  35-3 
+  3  55.8 

~  3  20.2 
+  0  o.g 

+  0  45-7 
+  0  12.4 

s 

—  37-5 
+  (67.5) 

—  20.0 

—  12.2 

+  5'.o 
+  II. 0 

s 

-  2.2 

+   2.2 

+   0.2 

-  J3.1 
+   6.3 

-  1.4 

m       s 

—  22  18.7 

+  4  2.8 

—  3  26.3 

—  o.i 
+    48.8 
+    II. 6 

-  21.0 
+  15.5 

-  26.8 

-  14.0 
+  54.0 
+  10.5 

J 

-  2-3 

+  2.7 

-  0-5 

-  13.9 
+   5. a 

-  I.I 

The  13  seconds  by  which  C  was  thrown  back  is  allowed  for  in  columns  A.  The 
discordance  of  H  seems  to  indicate  that  there  is  a  mistake  in  its  comparison  for  July 
23.0.  The  general  result  is  that  the  rate  of  A  agrees  very  nearly  with  the  mean  of 
the  other  rates,  while  the  discordance  of  H  and  M  are  such  that  it  is  impossible  to  say 
whether  the  correction  to  the  position  of  A  for  July  22.5  should  be  positive  or  nega- 


MBIHI 


RESEARCHES  ON  THE  MOTION  OF  THF  MOON.  1 87 

tive.     We  shall  therefore  suppose  the  rate  of  A  correct ;  its  corrections  will  be  found 
as  follows: — 

July  21.  July  23. 

Clock  times  of  0's  transit  (true  mer.)    .       8''  2""  24».5  8''    9™  53».3 

Mean  times o"  5"  49'.$  o"    5"  55'.4 

Clock-corrections +4"  3""  24".8  3"  S^""    2».i 

At  the  time  of  the  occultation,  the  difference  of  clocks  A  and  H  was  I3".3.  It 
appears,  therefore,  that  Heinsius  observed  the  occultations  about  i'.5  earlier  than 
Delisle.     Taking  the  mean  of  the  two  observers,  we  have : — 

e,  Imm.  01  Em.  61  Em. 

Clock-times  by  A        9"    5"  37'-9  9"  38"    7'-2  9"  50™  45'. 2 

Clock-corrections        3"  sT"  44"-o  3'  57"  38'-9  3"  57™  37'-i 

Mean  times     .     .       13"    3"  21 '.9  13"  35™  46'. i  i3"48»22*.3 

1738.    Jan.  2.    Occultation  of  Aldebaran  and  the  Hyaiies. 
Immersion  of /,  instantaneous.  fl' Tauri.  e' Tauri. 

2  observers  diff.  li*.        Sec.  of  app.  time. 

I  II  4S  B  *94  2  21  30J  5a 

6  26  2  D  l8  7  3S  34i  5'J 

I  9  47J  G  tSJ  2  19  32J  sij 

I  7  7  H  ao  2  17  4j  54 

I   10   28.5    J  18  2   20   I3J   -  S» 

I   3  16   K        l81        2  12  S9J        SI 

+    1-  • 

The  following  are  the  apparent  times  from  the  mean  of  all  the  clocks,  supposing  Delisle 
to  have  applied  the  right  clock-correction : — 
Immersion  of  /     6^  15°'  i8.'s 

0'     7    24    52.0    —  I* 
0^     7    28      8.0    —I" 
Aldebaran    12    18    46.0    — 0.5-    Emers.  12"  58"  25'-    Observer  thinks  right ;  but  the  other 
m     8    46    16  observer  is  put  down  lo"  later. 

1737.    Nov.  25. 

Transit  of  sun,  sextant 4"    7""  43'-'    ^ 

gnomon 4      7    34  -S    ^ 

G.-S -  8-6 

1738.    Jan.  3. 

Transit  of  sun,  sextant 7"    o-    7».6    B 

gnomon 6    59    59  -9    B 

G.— 8 -7-7 

Febr.   25.  Correction  of  gnomon  from  6  pair  altitudes    .    .  +2'-7 

March  19.  "  "  "  "  •    •  +6-8 

Jan.       2,  a.  m.    Transits  with  sextant. 

Spica i"  14"  37*       B 

Arcturus *     ^      Si 

p.m.    Algenib °     *    3»J 

Luc.  T »    SS      3 

i»  Hyadum 4     7    4* 

Aldebaran       4    23    4> 

Sirius 6    37     »3 


1 88  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

We  h.avo  to  adopt  Delisll's  appsirent  times.  Tlio  error  of  tlie  gnomon  is  quite 
uncertain,  so  that  tlie  times  are  also  uncertain.  A})plying  the  equation  of  time, 
which  ranges  from  +4"  45"- 5  to  +4'°  52'.o,  we  have  for  the  mean  times  of  the  phe- 
nomena :— 

71  Tauri,  immersion,  1738,  January  2 6'' 20°    4".o 

01 7''29"'38".5       , 

©a ' 7*"  32"  54".5         ■  '  ■; 

*  )»,  B.  A.  C.  1391  (f) 8''5i'"    3".5        '  :^ 

a    Tauri la"*  23"  37".8 

Em 13''    3"  i7'.8 

1738.     Febr.  2,  aoir. 

Imrnersiou  of  /  II  at i?*"     S'"  37'      H 

4     59     18       A  7"  ss"  34»  app.  t. 

Api)arent  time,  mean  of  four  clock.s     ...      7''  55'"  33"  i 
But  the  guoinou  is  supposed  correct. 

Sun  on  gnomon  Febr.  2 9''    2'"  27"     A 

"3 9      6    30       A 

1738,  Aug.      3.    Correction  of  gnomon +  7'-3 

"        19-  "  "  +5 .6 

1738,  Octb.     2,  soir,  occultation  d'Aldebaran. 

Immersion,  exact  at 0''  10"'     1.5'     H.     (2  observers.) 

Emersion i     10     27         H.     Observer  HErNSlus. 

'739)  Outb.    24,  matin,  occultation  tie  I'etoile  i  de  la  sixieine  grandeur  que  .Mr.  FiasisI'EED  appele 

la  boroalo  des  trois  qui  suivent  le  bras  droit  des  Jumeaux. 
Immersion  dans  la    partie  eclaire  de    la 

lune  -X' 3''  50°'  44»       B  ;!    " 

Presqn'il  la  precision  d'une  seconde. 

Moment  precise  de  I'emersion      ....     s""     i""  37"       B 

1739,  Octbr.  25,  niiitin.    Immersion <5Ciincri  (within  i  sec.)    3"  24'"  58'       B 

Emersion,  instantaneous    ...    4    31     32         B 
1741,  March  24.    A  midi  I'on  a  commence  a  observer  aujourdhui  le  passage  du  soleil  il  une  non- 
velle  mtiridicune  filaire  tracde  daus  le  grand  observatoire  superieiire,  pendule 

K  comuie  il  suit o"'  12™  404*  Mean  of  2. 

o    14     S98 

2     19-5 
The  usual  gnomon  I J  sec.  earlier    ...    o  13    50.0 

March  25,  soir,  immersion  ij  Oancri  o''  7'"  54"  K  (2  observers  agree  exactly). 

1741,  March    1.    Oor.    to    meridian  (gnomon)    per  double 

altitudes +    ij" 

April    25 +  6^ 

Merid.  superieuro +    i'3 

July     II.  Inf. +11,0 

Sup +   39 

Applying  +  7'o  for  correction  of  gnomon,  we  find  the  correction  of  clock  G  on 
mean  time  to  be; — 

August  8.  At     8''  55"'  2i».7  of  G,               con-.  =  +3''  9"  49'.6 

9.  At     8"  58"  4o".2  of  G,               coiT.  =  +3"  6™  23'.4 

The  clocks  appear  to  agree  so  well  that  no  reduction  of  the  others  is  necessary. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


189 


There  is,  however,  .an  obvious  mistake  of  4'  in  the  time  of  immersion  of  Aldebaran, 
as  given  by  G.  Interpohiting  clock-correction,  we  have  the  following  local  mean 
times: — 

1738,  Augusts.  Immersionof  71  Tauri  .  .  .  .  15"  3"  lo'.o 
Eir.rsionof  71  Tauri  ....  15'' 59""  5"-9 
Immersion  of  (9,  Tauri    ....     16^  21"  so\7 


Immersion  of  ©2  Tauri 

n  Tauri 

Immersion  of  a  Tauri 


16"  22" 
21"  18" 


r-7 

5'4 
22"    7"'49'-3- 


POSITIONS  OF  THE  MOON   PROM    HANSEN'S  TABLES,  USED  IN  COMPARING  THE 
PREOEDING  OBSERVATIONS  WITH  THEORY. 

When  a  number  of  places  of  the  moon  are  to  be  computed,  several  modifications 
may  be  made  in  the  use  of  the  tables,  whereby  the  labor  of  computation  will  be 
diminished.  " 

(i)  Omission  of  terms  unimportant  on  account  of  their  minuteness. 

The  older  observations  are  so  far  from  exact  that  there  is  no  advantage  in  cairy- 
!ng  the  computation  of  the  Fundamental  Argument  to  the  last  degree  of  precision. 
Portions  of  the  double-entry  tables  may,  therefore,  be  omitted  in  comparing  such 
observations  with  theory.  The  minuter  terms  are  those  contained  in  the  twenty-seven 
tables  of  double-entry:  all  or  a  part  of  these  tables  may  be  omitted  with  the  following 
results : — 

If  the  twenty-seven  double-entry  tables,  XII  to  XXXVIII,  are  all  omitted,  and 
the  sum  of  their  constants,  0.0022240,  substituti  d,  the  probable  deviation  of  the  com- 
puted longitude  from  that  given  by  a  rigorous  computation  will  bo  ±i3"-6 

If  the  seventeen  tables,  XXII  to  XXXVIII,  are  omitted,  and  the  sum  of  their  con- 
stants, 4290,  substituted,  the  probable  deviation  will  be  ±2".7- 

If  the  nine  tables,  XXX  to  XXXVIII,  are  omitted,  and  the  constant,  1 140,  sub- 
stituted, the  probable  deviation  of  the  result  will  be  ±o".85.* 

(2)  Modifications  tvhen  many  places  of  the  moon  arc  to  he  computed. 

These  modifications  refer  principally  to  the  formation  of  the  arguments,  and  the 
introduction  of  the  terms  of  long  period.  They  are  applicable  when  places  of  the 
moon  are  required  for  a  series  of  dates  in  which  there  is  no  interval  greatly  exceeding 
a  year.  The  following  is  a  description  of  the  method  of  forming  the  arguments  actu- 
ally adopted  for  the  years  after  1632. 

The  dates  were  divided  into  groups  of  not  more  than  ten  or  twelve,  except  in 
cases  where  a  number  of  dates  were  crowded  together,  when  the  number  might  be  a 
little  greater.  A  group  always  had  to  terminate  when  an  interval  of  much  more  than 
one  year  was  encountered.     When  no  such  interval  occurred  for  several  successive 

'  U  is  to  lie  remarked  that  in  cases  where  an  approximate  position  of  the  moon  is  rcquireil  for  any  purpose.this  plan  of 
using  Hansen's  Tables,  with  the  omission  of  the  smaller  terms  (always  taking  care  to  include  the  constant  terms  of  the  omitted 
tables),  is  much  better  than  that  of  using  the  older  tables,  the  elements  of  which  are  affected  with  unknown  systematic  errors. 


IQO 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


groups,  the  same  date  was  taken  as  tlie  last  of  one  group  and  the  first  of  the  group 
following. 

All  the  arguments  were  then  computed  for  the  limiting  dates';  "  each  group  in  the 
usual  way.  Those  of  single  entry,  including  g  for  the  intermediate  dates,  were  then 
found  by  adding  to  those  for  each  date  the  interval  in  days  between  that  and  the  date 
next  following,  and  subtracting  the  greatest  number  of  entire  periods  contained  in  the 
sum.  The  double-entry  arguments  are  constant  for  each  period  of  g,  and  change  by 
a  definite  amount  for  every  new  period.  To  pass  from  those  for  one  date  to  those  for 
the  date  next  following,  it  was  only  necessary  to  add  or  subtract  a  number  depending 
on  the  number  of  periods  of  g  which  had  terminated  during  the  interval.  To  enable 
this  to  be  done  with  the  least  labor,  and  risk  of  error,  a  long  slip  of  paper  was  prepared 
for  each  number  of  periods  of  g.  On  the  bottom  of  each  slip  was  written,  in  regular 
order,  the  quantity  by  which  each  argument  increased  during  the  number  of  periods 
coiTesponding  to  the  slip.  On  the  opposite  side  and  edge  of  the  slip  were  written,  in 
red  ink,  the  complements  of  these  numbei's;  that  is,  the  quantities  by  which  they  fell 
short  of  one  period  of  the  argument.  Then,  to  pass  from  the  values  of  the  arguments 
from  one  date  to  those  for  the  succeeding  one,  the  number  of  entire  periods  of  g  which 
had  been  subtracted  was  noted,  and  the  con-esponding  slip  taken.  Being  laid  over 
the  row  of  arguments,  the  red  numbers  were  first  subtracted  in  all  cases  where  they 
were  less  than  the  argument.  Then,  turning  the  slip  over,  the  black  numbers  were, 
added  in  all  the  remaining  cases. 

When  the  end  of  the  group  was  reached,  the  series  of  arguments  thus  obtained 
was  compared  with  those  derived  by  direct  computation;  and  if  they  agreed,  which 
was  nearly  always  the  case,  the  intermediate  arguments  wore  all  considered  correct. 
The  only  way  in  which  they  could  be  erroneous  would  be  by  two  opposite  and  equal 
errors  entering  into  the  same  series.  The  computer  who  formed  the  arguments  in  this 
way  was  the  Rev.  Parker  Phillips,  whose  conscientiousness  and  accuracy  were  such 
as  to  inspire  entire  confidence  in  his  work. 

(3)  Terms  of  long  period  produced  by  Ventis. 

The  variation  of  these  terms  is  so  slow  and  regular  that  it  is  much  easier  to  include 
their  sum  in  the  original  computations  of  the  arguments  than  to  compute  and  add 
them  for  each  date.  Their  sum  was,  therefore,  computed  for  the  beginning  of  every 
tenth  year,  and  inteipolated  to  every  year,  as  shown  in  the  next  table.  Their  product 
by  the  proper  factors  to  form  the  corrections  to  Arguments  32  and  33  was  also  com- 
puted, and  included  in  the  same  table.  These  arguments  are  farther  to  be  corrected 
on  account  of  the  terms  of  long  period  con-esponding  to  Arguments  28  and  29;  but 
the  en'or  from  omitting  these  terms  is  so  small,  scarcely  o".  i  in  the  mean,  that  they 
have  been  neglected.  In  place  of  them,  the  constant  quantities  -j-  200  and  + 1 86  have 
been  included  in  the  table. 

The  addition  of  these  corrections  to  the  three  leading  arguments  necessitates  a* 
correction  corresponding  to  their  change  duriiig  the  interval  between  two  consecutive 
dates,  to  be  applied  to  that  interval  in  order  to  find  the  total  change  of  the  argument. 
The  amount  of  this  change  for  100  days  in  units  of  the  last  place  in  the  argument  is 
tabulated,  and  shown  in  the  table  next  following  that  last  described. 


RESEARCHES  ON  tHE  MOtlON  OF  THE  MOON. 


I9t 


The  explanation  of  the  several  parts  of  the  table  is  as  follows: — 
Column  A  g  gives,  for  the  beginning  of  each  year,  the  sum  of  Hansen's  Venus-terms 
of  long  period,  as  derived  from  Tables  XLI  and  XLII,  Arguments  30  and  31,  without 
any  modification. 

The  precepts  of  the  tables  direct  that  Arguments  32  and  33  be  corrected  by  the 

sum  of  the  four  Tables  XXXIX  to  XLII  inclusive,  multiplied  by  the  factors  o.i  1545 

and  0.10717  respectively.     The  sum  of  the  first  two  tables  diff'ers  so  little  from  that  of 

their  constants,  1735,  that  we  may  use  the  latter;  we  have  therefore  put 

A  32  =0.11545  (Ar/  +  1735)  =0.11545  A5f  +  2oo 

A  33  =  0.10717  (A /7  + 1735)  =0.10717  A  (/  + 186. 

Arguments  32  and  33  are  to  be  corrected  by  these  quantities  respectively. 

The  change  of  g  between  two  consecutive  dates  varies,  not  only  in  consequence 
of  the  variation  of  A  g,  but  of  tho  secular  acceleration.  The  change  of  the  variation 
in  the  seventh  decimal  place  of  g  for  100  days,  in  order  to  reduce  it  to  the  adopted 
period  corresponding  to  the  epoch  1800,  as  arising  from  both  these  sources,  is  as 
follows: — 


Date. 

Secular 
Term. 

Venus 
Terms. 

Date. 

Secular 
Term. 

Venus 
Terms. 

1620 

-103.31 

-     4. II 

1710 

-  51.72 

+  30.62 

1630 

-  97.58 

+     4.06 

1720 

-  45.98 

+  24.85 

1640 

-  91.85 

+   12.23 

J  730 

-  40.24 

+   17." 

1650 

-  86.12 

+   1993 

1740 

-  34.49 

+     8.04 

1660 

-  80.39 

+  26.50 

1750 

-  28.74 

-     1.71 

1670 

-  74.66 

+  31.61 

1760 

—  22.99 

—  IJ.64 

1680 

-  68.93 

+   34.79 

1770 

-  17.25 

—  21.10 

1690 

-•  63.19 

+  35.70 

1780 

—  11.50 

-  29.46 

1700 

-  57.46 

+  34.30 

1790 

-     5.75 

-  36.09 

1710 

-  51.72 

+  30.62 

1800 

0.00 

-  40.50 

The  sum  of  these  terms,  interpolated  to  the  beginning  of  each  year,  is  given  in 

the  table  as  ^4^,  while  the  corresponding  terms  for  correcting  Arguments  32  and  33 

dt 
follow.     To  find  the  change  of  g  and  of  Arguments  32  and  33  between  the  epochs 
<  and  <  +  A  <,  it  is  necessary  to  take  out  the  values  of  these  three  derivatives  for  the 
time  f  +  J  A  f,  when  we  shall  have: — 

-     ChangeofArg.  =  A<  +  ^.-^-^^--iX  Period; 
it  being  remarked  that  the  second  term  is  given  in  units  of  the  last  place  of  decimals. 


192 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Date. 

1630 

31 
32 

33 
34 
35 
36 
37 
38 
39 
1640 

41 
4« 
43 
44 
4S 
46 

47 
48 

49 
1650 

5' 
52 
53 
54 
S5 
56 
57 
58 
59 
1660 
61 
62 
63 
64 
65 
66 

67 
68 

69 
1670 

71 
7a 
73 
74 
75 
76 
77 
78 
1679 


3289 
3304 
3322 

3343 
3368 

3396 
3428 

3464 
3503 
3545 
3590 
3637 
3686 
3738 
3793 
3851 
3912 
3975 
4041 
4110 
4182 
4257 
4335 
4416 
4500 
4586 
4674 
4763 
4854 
4947 
5043 
5141 
524' 
5343 
5447 
5554 
5663 

5774 
5887 
6002 
6119 
6237 
6356 
6476 
6598 
6721 
6845 
6970 
7096 
7223 


Diff. 


15 

18 
21 

25 
28 
32 
36 
39 
42 
45 
47 
49 
52 
55 
58 
61 

63 
66 
69 
72 
75 
78 
81 
84 
86 
88 
89 
9> 
93 
96 
98 
100 
102 
104 
107 
109 
tii 
"3 
115 
117 
118 
lig 
120 
122 
123 
124 

125 
126 
127 
128 


A  32 


580 
581 

583 
585 
588 

591 
595 
600 
604 
609 
614 
619 
624 
630 

637 
644 
651 
658 
666 
674 
683 
6gi 
700 
709 

7'9 
729 
740 
750 
761 
772 
782 
793 
805 
817 
S29 
841 

854 
866 
879 
892 
905 
918 
932 
947 
961 

975 
990 
1004 
1019 
1033 


'i  33 


539 
540 
542 
544 
547 
550 
554 
557 
562 
S66 
571 
576 
582 
587 
593 
599 
606 
613 
620 
627 
635 
643 
651 
659 
668 

677 
687 
696 
706 
7i6 
726 
737 
748 
758 
769 
780 
792 
805 

817 
830 
842 

855 
867 
880 

893 
907 
920 
933 
947 
960 


St 


36.5 
35.7 
34-9 


+  8.1 

8.1 

+  8.1 


rfA33 

dt 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


'93 


Date.   A  g 


1680 
81 
82 

83  I 

84  i 


85 


86 

87 

88 

89 

l6go 

91 
92 

93 
94 
95 
96 

97  i 

98  I 
1699 
1700 

01 
02 
03 
04 

05 
06 

07 

08 

09 
1710 
II 
12 
13 
14 
J5 
16 

«7 
18 

>9 
1720 
21 
22 
83 
«4 

as 
26 
27 

28 
1729 


735> 
7480 
7609 

7739 
7869 
8000 
8131 
8262 

8394 
8526 
8653 
8789 
8920 

9051 

9182 

9312 

9442 

957> 

9700 

9828 

9956 
10083 
10209 
10333 
10456 

10578 
10698 
10816 
10933 
11048 
11161 
1 1274 
1 1 386 

11495 
1 1 602 
11707 
1 1 809 
11909 
12006 
12101 
12193 
122S2 
12369 
12453 
12535  I 

12615  ; 
12692  I 
12767  I 
12839  I 
12908 


Ui(T.   4  32 


129  { 

129  '■ 

130  ' 

130  i 

131  ! 
131  I 

131  : 
132 

132  : 
132  I 
131  i 
i3>  \ 
131 
131 
130  i 
130  '. 
129 
129 
128 
128  j 
127  i 
126  ' 
124 
123 
122  I 

120  I 

118 

117 

115 

113 

113 

112 

109 

107 

105 

102 

100 
97 
95 
92 
89 
87 
84 
82 
80 
77 
75 
72 
69 
66 


1049 
1064 
1079 
1094 
I10() 

1124 
1 139 
1154 
1169 
1185 
1200 

1215 

1230 

1245 

1260 

1275 

1290 

1305 
1320 
1335 
1349 
1364 
1378 
1393 
1407 
1421 
1435 
1449 

1462 

1475 
1488 
1500 
1513 
1526 
1538 
1551 
1563 
"574 
1585 
1596 


4  33 


973 

987  ' 
1001 
1015 
1029 
1043  , 
1057 
1071 
1085 

1099 ; 

1113 
1127 
1142 

1156  j 
1170  ' 

1 184  1 
1198  I 

1212 

1226  . 
1240  I 
1254  I 

1263  ; 

I23l  I 

1295  \ 

1308  i 

1321 

1334 

1346 

1358 

1370 

1382 

1394 

1406 

1417 
1423 

1439 
1450 
1461 
1471 
1481 


1607  j  1491 

1617  I  1500 

1627  \  1510 

1637  1519 

1647  1528 

1656  !  1537 

1665  j  1545 

1673  I  1553 

1682  i  1562 

1690  1  1569 


dt 


341 

33-4 
32-6 
319 
31.2 
30.5 
29.9 
29.3 
28.7 
23.1 
27-5 


1  ^ 

</A32 

dt 

+  8.1 

8.1 

8.1 

8.1 

8.1 

8.0 

8.0 
7-9 
7.9 

7.8 
+  7.8 


</i33 
dt 


+  1.9 
1.9 
2.0 
2.0 
2.0 
2.0 
2.0 
2.0 
2.1 
2.1 

4-    2.1 


23.2 
22.3 
22.5    j 

22.2  ! 

22.0  I 

21.3  I 
I 

21  .6 

21.4 

21.3 

21.2 
21.1 
21.1 

21. 1 
21  .0 
21.0 
21.0 
21.0 
21.0 
21.1 
21.1 
21.1 
21.2 
21.3 
21.4 
21  .6 
21.3 

22.0 

22.2 
22.5 
22.3 


7-3 
7-3 

7.2 

7.2 

7.> 
7.0 
6.9 
6.9 
6.8 
6.7 
6.6 

6.5 
6.4 
6.3 
6.2 
6.1 
6.0 
5.9 
5.8 
5-7 
5.6 
5-5 


•t-  2.1 
2.1 
2.1 
2.0 
2.0 
2.0 
2.0 
1.9 
1.9 
1.9 
1.9 
1.9 
1.8 
1.8 
t.7 
1-7 
1.6 
1.6 
1-5 
1-5 
1.4 
1.4 
••3 


5.3 

1.3 

5-2 

1.3 

51 

1.2 

5-0 

I.I 

4.8 

I.O 

4-7 

I.O 

+  4.6 

+ 

0.9 

25- 


-75  Af.  2 


194 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Date, 

Aa' 

Difr. 

A  32 

A  33 

at 

7.32 
,11 

./  33 
lit 

1730 

12974 

61 

169/ 

1576 

-   23.1 

+   4.4 

+   0.8 

3> 

13015 

58 

1705 

•  583 

234 

43 

0.8 

32 

>3"93 

1711 

1590 

23.7 

4-3 

0.7 

33 

13148 

55 
52 

1718 

1596 

24.0 

4.0 

0.6 

34 

13200 

1724 

1601 

24.4 

3.9 

"•5 

35 
3& 

13249 
13294 

49 
45 
42 
38 
36 

32 

2B 

1730 
1735 

1607 
l6l2 

24 .7 
25.0 

3-7 
3.6 

0.4 
0.4 

37 

13336 

1740 

1616 

25.3 

3.4 

0.3 

38 

13374 

1744 

1620 

25.7 

3.3 

0.2 

39 

1740 

"3410 
13442 

1748 
1752 

1624 
1627 

26.0 
26.4 

31 
3.0 

+  0.1 
0.0 

41 

13470 

24 
21 

17 
14 

1755 

1630 

26.3 

2.9 

-  0.1 

42 

13494 

1758 

1633 

27.2 

2.8 

0.2 

43 

13515 

1760 

1635 

27.6 

2.6 

0-3 

44 

13532 

1762 

1637 

28.0 

2.5 

0.4 

45 

13546 

1764 

1638 

28.4 

2.3 

0-5 

46 

13556 

10 

7 
+   3 

1765 

1640 

28.3 

2.1 

0.6 

47 

13563 

1766 

1641 

29.3 

2.0 

0.7 

48 

13566 

1766 

1 64 1 

29.7 

1.8 

0.3 

49 

13565 

4 
g 

1766 

1640 

30.1 

1-7 

0.9 

I--0 

13561 

1765 

1640 

30.5 

1-5 

1.0 

51 

'3553 

12 

1764 

1639 

30.9 

1-4 

I.I 

52 

'3541 

1762 

1638 

31-3 

1.2 

1.2 

53 

13526 

15 
19 

1760 

1636 

31.8 

t.i 

1-3 

54 

13507 

1758 

1634 

32.2 

0.9 

1.4 

55 

13484 

23 
26 

■756 

1631 

32.6 

0.8 

1-5 

56 

13458 

1753 

1628 

33-0 

0.6 

1.5 

57 

13428 

30 

1750 

1625 

33-4 

0.5 

1.6 

58 

13394 

34 

37 
42 

45 
48 
52 

55 

1746 

1 62 1 

33.8 

0.3 

1.7 

59 

13357 

1742 

1617 

34-2 

+  0.2 

1.8 

1760 

13315 

1737 

1612 

34.6 

0.0 

1.9 

61 

13270 

1732 

1608 

35.0 

—  0.2 

2.0 

62 

13222 

1727 

1603 

35-4 

0.3 

2.0 

63 
64 

13170 
13115 

1721 
17'5 

1597 
1591 

35-8 
36.1 

0.5 
0.6 

2.1 
2.2 

65 

13056 

59 
62 

66 

1703 

1585 

36.5 

0.8 

2.3 

66 

12994 

170I 

1578 

36.9 

0.9 

2.3 

67 

12923 

69 

1693 

•571 

37.2 

I.O 

2.4 

63 

12859 

1685 

1564 

37.6 

1. 1 

2.5 

69 

12787 

72 
76 
80 

83 

86 

89 

1677 

1557 

38.0 

1.2 

2.6 

1770 

12711 

1668 

1549 

38.3 

1-4 

2.7 

71 

1 263 1 

165S 

"540 

38.6 

1-5 

2.7 

72 
73 

12548 
12462 

1649 
163;, 

1531 
1522 

38.9 
39  2 

1-7 
1.9 

2.8 
2.9 

74 

12373 

1629 

1512 

39.5 

2.0 

3.0 

75 

12281 

92 

1618 

1502 

39-8 

2.1 

3-0 

76 

12186 

95 
98 

1607 

1492 

40.0 

2.3 

3.1 

77 

12088 

1595 

1481 

40.3 

2.5 

3.2 

78 

79 
1780 

11987 
11883 
11776 

lOI 

104 
-107 

1584 

1471 

-  40.6 

-  2.7 

-  3-3 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


•95 


TliG  tenn«  oniittod  were  as  follows: — 

For  all  the  Aral)imi  ul)S('rviiliniis  and  tor  those!  of  I'toi.i.mv,  nil  the  (hnihle-ciitry 

tables  were  omitted. 

From  1621  to  1666,  Tiildes  XXll  to-'XXXVlII  of  doiil)le-(iitry  were  omitted. 
In  all  cases  of  such  omission,  the  sum  of  the  ('oustaiits  inehided  in   the  tables 

was  added. 

From  167 1  onward,  all  tiui  tables  wt^re" included. 

Still  another  modification  consists  in  the  omission  of  the  nutation.  Since  the 
comparison  of  the*  place  of  the  mooi:  with  that  of  the  sun  or  star  was  made  in  lon- 
gitude, the  ecpiinox  to  which  each  was  referreil  was  indilfcreiit ;  tlie  mean  eepiinox  of 
the  date  has  therefore  been  chosen.  The  nutation  terms  l)eino'  given  in  'I'aldes  VII 
and  IX  of  LoiifiUndc  Vrai,  these  tables  were  omitted,  amithe  sum  of  the  constants, 
o''. 00550,  substituted. 

After  the  formation  of  the  arguments,  the  computations  of  longitude,  latitude, 
and  parallax  were  made  in  duplicate  Ijy  two  independent  computers,  and  the  work 
was  then  compared  Ity  myself  Where  differences  of  importance  were  found,  the 
computer  who  was  wr mg  correlated  his  work  without  reference  to  tl-.at  of  the  other. 
That  these  i)reeautions  have  secured  al)solute  freedom  from  error  cannot  bo  asserted. 
Discrepancies  of  various  sorts,  which  dctveloped  themselves  in  the  final  results,  led  to 
the  discovery  of  some  errors  which  escaped  all  the  i)reliminary  examination,  and 
which  are  wm-thy  of  mention  as  atlbrding  hints  to  others.  In  one  instance,  an  error 
of  20  days  in  forming  an  argument,  though  marked  as  wrong,  failed  to  be  corrected. 
About  half  a  groiii)  of  laiitudes  (dates  83  to  91)  were  in  error  from  this  cause.  In 
another  instance,  some  inadvertence  in  attemjiting  to  correct  an  error  led  to  a  connnon 
error  in  two  computations.  In  a  third  instance,  a  typographical  error  in  the  tables  led 
to  both  computations  of  longitude  being  wrong  i)y  about  20".* 

This  last  source  of  error  is  that  which  I  now  most  fear.  Througli  sonui  over- 
sight, some  of  the  volmnes  of  tables  used  by  the  computers  did  not  have  tlu^  typo- 
gniphical  errors  corrected.  Such  errors  in  tiie  longitude,  if  important,  will  admit  of 
detection  where  two  longitudes  with  the  difl'erent  variations  are  computed  for  the  same 
day;  and  it  was  by  comparing  the  difference  of  two  longitudes  with  the  variations 
that  the  mistake  above  nu'Utioned  was  found.       _^ ^^ 

•  In  mv  prelin.inarv  paper  in  the  .h„,;„,n,  J,,m,.il  of  Sdaue  nml  Arh  for  S.-ptemher.  1870,  tlie  occuUation  of  Alde- 
baran  on  iftSo,  Xovcmhor'?,  appc.us  as  unaccjunUiWy.lUcor.lant.  The  ailTicully  arose  from  a  typ..i;r.->ph.cal  error  of  i  in  the 
t«t)ular  prineipal  term  of  latitude. 


196 


RKSEARCHKS  ON  THE  MOTION  OK  Till;  MOON. 


Sun'n  Ococcntric— 

.Mo(.n' 

s  (ieoccniric — 

• 

Year. 

Dale. 

(ircenwieli 
Mean  Time. 

I.onKilude. 

.'•enii- 

LoliKituile. 

Motlun  in 

Paral. 
lax. 

Mean  l",i|uin. 

dlnni. 

Mean  E<|Uln. 

0^.01. 

Laiiiuue. 

-  720 

M.ir. 

19 

//   m     s 
500 

35"   31   3"-4 

15  57 

17"  59  3". 9 

7  34  32 

+ 

"     3  39 



55  44 

-  719 

Mar, 

8 

8     0    0 

34"  41   49. 4 

ifi     0 

If)"  30  31.7 

7     6.02 

T- 

0  46  43 

53  55 

-  719 

Sept. 

I 

300 

150  54  28.0 

if)     0 

329  55  25.4 

9     4.97 

- 

"  37  45 

61    10 

—  630 

April 

31 

13    0    0 

24  23  3f).8 

15  49 

3"4    If.    1 1 . 0 

7    f'.78 

+ 

0  53  50 

54    a 

-    582 

July 

16 

800 

106  33   14,6 

.5  48 

38f)  37  13. 1 

7   II . in 

"  4"  53 

54  14 

-    501 

Nov. 

") 

800 

231   54    14.  f) 

If.  16 

51  46  47.6 

7     5  "2 

+ 

"  5"  43 

53  51 

—    490 

April 

25 

7     0    0 

38  31   35.9 

15  49 

207  55  48.9 

8     7.91 

+ 

I     I   36 

57  48 

-    3S2 

Dec. 

33 

'    16    0     0 

2f>7     t   57-5 

I6  17 

8f.  4'.  52.5 

8  42.95 

_ 

"  57  49 

59  52 

-    38. 

June 

18 

400 

80  37  49.9 

.545 

35947     0.2 

7  i".34 

+ 

0  46  38 

54  " 

-    381 

Dec. 

13 

600 

35fl     9  56.4 

If)  17 

75   12  47-" 

9     8.24 

— 

0  31    10 

61    30 

—  aoo 

Sept. 

33 

5     0    0 

I7f'     0  41.3 

If.     4 

356  2"  25.1 

7  28.60 

+ 

0  33   38 

55  23 

-    199 

Mar. 

■9 

800 

355    23   32. f) 

15  58 

173  5fi  33.8 

8   16.66 

+ 

0    4  54 

58   19 

—  199 

Sept. 

II 

10    0     0 

165      I    43.1 

If)      3 

343  55     3-4 

8   19.93 

f 

007 

58  30 

-  173 

April 

3" 

10    0     0 

35  40     6-5 

15   49 

314  45   55.5 

9     4.43 

— 

0  35  42 

61     5 

-  140 

Jan. 

37 

f)    0     0 

304  3t  5fi-3 

If)    13 

123  2f.  23.7 

9     8.10 

+ 

0  46  34 

61    30 

+  125 

April 

5 

600 

14  ifi  ir.9 

15  54 

194     2  38.5 

8   18.60 

+ 

"  57  26 

58  36 

133 

May 

6 

800 

44  II  33.5 

15  48 

333  5f>     8.0 

7  20.03 

— 

0  35  40 

54  50 

'3-) 

Oct. 

20 

8     0     0 

:o6  15    f).3 

16  II 

35  54  53-2 

7  33.38 

— 

0  36  45 

55  40 

,36 

Mar. 

5 

1200 

344  36  35.8 

16      3 

163  51   50.9 

8  53.37 

— 

0  53  II 

60  28 

829 

Nov. 

39 

16  36  14 

252  37     1.4 

If)    15 

251  37  35-6 

7  51.53 

+ 

0  33     7 

56  54 

829 

Nov. 

29 

13  3fi  54 

252  41  432 

16    15 

252  38     3.6 

7  52.27 

+ 

0  16  49 

56  56 

854 

AUR. 

1 1 

12     I     7 

143  35  32.2 

15    52 

321  40  199 

8  48.28 

+ 

0  18  14 

60  16 

856 

June 

31 

12  21   58 

04  10  31;. 2 

15  45 

273  34  3o-fi 

8  15.06 

- 

0  45    13 

58  14 

923 

June 

I 

b  56  33 

74  43  21.5 

15  4f> 

255  29  5" .2 

8  37-3" 

— 

0  43  50 

59  34 

923 

Nov. 

10 

16  21     8 

23?    2(.  48.7 

16  14 

232  37  16.1 

9    4.21 

+ 

0  33  33 

61    16 

923 

Nov. 

10 

17  32  32 

233  29  49-5 

16   14 

333  33  33.0 

9     407 

+ 

0  38  14 

61    II 

935 

April 

II 

2  38  3(1 

26     7  56.1 

1554 

304  16  46.0 

a  25.73 

+ 

0  36  51 

58  57 

925 

April 

" 

7  47  49 

26  20  33.1 

15   54 

307  18  22.5 

8  37.80 

+ 

0  30     2 

59    6 

927 

Sept. 

'3 

12  50  46 

175   II   58.9 

16     0 

354  38  43.6 

9     5-48 

+ 

0  51   14 

61   17 

928 

Auk- 

■7 

15  39  29 

149  36  57-7 

15   53 

149     7  31.6 

7  51.39 

— 

0  13  10 

56  54 

929 

Jan. 

27 

8     5  32 

313  14     7-1 

If.   13 

131  48  27.9 

8  30.55 

+ 

0  30  37 

59  17 

933 

Nov. 

A 

'3  17  45 

227  48  52.7 

If.   13 

46  54  43-2 

7  14.45 

— 

0     5  53 

54  31 

977 

Dec. 

13 

18  19     2 

367     I  39  0 

If.  17 

365  49     0.3 

9    6.65 

+ 

0  35  14 

61  35 

977 

Dec. 

12 

30  36    10 

2f)7     7  28.7 

•16   17 

367   16     6.3 

9    6.38 

+ 

0  27  16 

61  35 

978 

June 

8 

0  33   39 

81  4S  SI.*-) 

15  45 

81    58   38.1 

7     6.34 

— 

0    6  10 

53  57 

978 

June 

8 

3    43    13 

81   54  24.5 

15  45 

83     7  17-5 

7     5.97 

+ 

0    0  16 

53  58 

979 

May 

14 

5  52     0 

57  5f)  59.6 

15  48 

238  51     9-2 

8  18.34 

+ 

0  32  36 

58  31 

979 

May 

28 

4   12  58 

71    "5     6-9 

15  46 

;i  47  32.3 

7  36.34' 

+ 

0  39     3 

55  55 

979 

Nov. 

6 

8     3  40 

22Q   27      8. 9 

16  13 

48  42  43.9 

8  18.33 

- 

0  37  36 

58  34 

979 

Nov. 

6 

II   18     0 

229  35  21.4 

16  13 

50  34  49" 

8  17.30 

— 

0  27  15 

58  38 

980 

May 

2 

14  26     0 

47  31    iS-fi 

15  49 

228  24  21.3 

7  38*20 

_ 

0   13      2 

55  36 

981 

April 

31 

13  28     0 

36  39  56-3 

15  52 

216  n  56.3 

7     5.32 

— 

0  45  50 

53  55 

981 

Oct. 

15 

14     7     0 

208     I   33.9 

16     8 

27  24  21.5 

9     2.06 

+ 

0  46  36 

61     7 

983 

Mar. 

I 

9  55     0 

346  13   '8.5 

16     5 

165  18  39.2 

8  38.20 

+ 

0  31  50 

59  43 

983 

Mar. 

I 

13  40     0 

346   22    36.4 

16     5 

lf'7  33  37.9 

8  36.75 

+ 

0  19  34 

59  35 

985 

July 

20 

2  56  30 

122    17    35.7 

15  47 

132  43    17.6 

8  10.32 

+ 

0  15     4 

58     I 

985 

July 

20 

4  iS  13 

122    20    51.7 

15  48 

123   29   43.1 

8  10.89 

+ 

0  10  50 

58     3 

986 

Dec. 

18 

'4  53     0 

272  49     I.O 

16  17 

92    16  49.4 

7     5.9" 

+ 

0  30  16 

53  58 

•    990 

April 

12 

-  42     0 

27  34  15.2 

15   54 

206  43  569 

7     6.15 

— 

0  37  39 

53  59 

qjo 

April 

13 

4     0 

27    42    24.7 

15  54 

200  23  26.7 

7     5-94 

— 

0  38  17 

53  59 

993 

Aug. 

19 

17  36     5 

151    54    39.6 

15  53 

'5"  28  33.5 

9     2.4" 

+ 

0     5   17 

fil     4 

1002 

Mar. 

I 

9  4r  18 

346  35  57.9 

lO     5 

165  37  27.9 

9     8.07 

— 

0    13       7 

61  37 

1004 

Jan. 

23 

I  51    0 

308  43  17.5 

16  14 

296     I   56.8 

8  32.44 

— 

I      2      7 

59  20 

1004 

Jan. 

24 

I  5'     0 

309  44      2.2 

16  14 

310    9  24.9 

8  23.57 

1 

+ 

0    15    51 

58  50 

"■~T 


RESEARCIIKS  ON  THE  MOTION  OF  THE  MOON. 

ic    I  Motion  In' 


No. 


I 

9 

3 

4 

A" 

i 

6 

7 
8 

9 

10 

II 

13 

13 
J4 
«5 
lO 

"7 

17" 

l8 

>y 

30 
21 

2  III 

21J 

22 

23 

24 

25 

26 

27 
2S 
21) 

30 
3> 

32 

33 

34" 

34* 

34 

35 

36 

37 

38 

3y 

40 
41 
42 
43 


Dale 


i     (Irfi'iiwiili  ^t(•:ln      ;     riCDCcnlrlc     |  Motion  In '     Geocentt 

UiiiK-nlMu'iii.       o''.oi.        Lai.  of  Moon. 


Ifi2i,  May  2o 

l623,  July    5 

1627.  June  17 

'•    Sept.  18 

1630.  June  10 

1632,  Fel).    5 

1633,  Feb.  14 
"     Apr.    8 

1634,  Dec.  30 

1635,  Aug.  26 
1637,  Mar.  2() 
if';*,  Jan.  24 

'■     Dec.  20 

1639,  Apr.    7 

"     June    I 

1641,  Apr.  13 

1644,  Nov.  14 

1645,  Aug.  21 

"     Oct.     7 
"     Oct.     8 

1647,  Jan.  20 
"     Apr.  12 

1652,  Apr.  7 
"     Apr.    8 

1654,  Aug.  II 

1656,  Jan.  26 

"     Mar.    I 
1658,001.  14 

t66o,  Apr.  26 

"     June  17 

1661,  Mar.  2q 

"     Mar.  30 

"     Aug.   3 

1663,  Mar,  14 
"     Aug.  18 

1664,  Mar.  31 
1666,  July     I 

1O71,  Mar.  14 


(ireenwi 

•li  Mean      ; 

Tiini'. 

A   m    s 

1 

18  3')  34 

•7774768  : 

31     5  10 

.S7S787C) 

1    9  24  '6 

.3i)'85") 

10    8  14 

.4233843 

10  39  30 

4  48  o 

7  12  o 

1 5  o  0 

11  20  4 

4  48     o 

5  43  44 
()  34  32 
<J     O     O 

7  17  49 

16  7  42 

9  o  21 
3  36  o 
()     o     o 

8  3  43 
15  36    o 

000 
300 

15      O     O  ] 
12       O      O 

15    o    o  I 
14  24     o  j 

10  O     O   I 

21  3C      O  j 
000; 

20  O 

22  24 

o  30 
2  54 
7   20 

9  52 

13  23  51 

9  41  39 
2100 

23  24 

21  o 

33  24 

7  15 
S     o 

8  o  57 
8  50  52 
8  25     o 

17  36    o 

20    o    o 

7  46    o 


■  437'>37' 

.2(MMK_XX) 
.  3(KX)()l)<) 
.62504)00 
.4722685 
.2000000 
.2387037  ' 

•3919'55 
.375fKxx) 

•  3040394 
.6720139 

•3752431 
. 1500000  ' 
.2500<xx) 

•3359'43 
,6500000 
.0000000 
.1250000 
.6250000 
.5ooo<xx) 
.6250000 
.6ooo(xx) 
. 4 1 66667 
.9000000 
.0000000 
•8333333 
■9333333 
.0208333 
.1208333 

•  3056597 
,4111806 
,5582292 
,4039236 
.8750000 
.9750000 
.8750000 
.9750000 
. 3020833 
•3333333 
•3339931 

•  3686574 
.3506944 
.7333333 
•8333333 
,3236111 


59  5  58. 7 

60  25  46.4 
198  24  43.4 
«44  5"  53-2 
278  37  23.8 

79  '  137 

80  22  11.4 
136  35  3.0 

46  6  19.3 
20  7  46.5 

54  24  14.8 
316  31  29.9 

55  14  22.7 
54  34  6.4 
90  38  16.8 
67  33  17^6 

70  37  53-0 

71  56  22.8 

63  55  47.3 
66  15  48.3 

148  43  39.6 

150  24  10.0 

^i  21  48. I 

64  643.9 
66  6  7.5 

123  56  43.0 

119  30  52.4 

18  36  33.0 

20  4  37.0 

138  21  50.1 

139  45  47.6 

306  8  52.3 

307  19  35.1 
44  7  192 

61  25  33.8 
238  38  39.5 
199  o  32.9 

9  36  33-8 
II  6  20.2 

24  28  26. I 

25  56  45 ■ 6 
237  8  42.2 

62  53  20.6 
325  32  18.9 

325  58  59- > 
65  40  39.2 

99  '3  35^o 

100  33  20,2 

46  28  53.4 


7  53.11 

7  54.05 

8  18.02 

7  5'-53 

7  1999 

8  5^2l 
8  6.25 
7  58.98 

7  22.32 

7  53-90 

8  11.76 
8  3;. (XI 
8  38.44 

8  17.34 
S  32.60 

7  36.62  , 
7  50.59  j 

7  51.67  ! 

7  5.41  t 

9  403 

8  7.94 
8  6.94 
3  52.87 

8  49.06 
o  48.26 

9  9-47 
8  38.18 
8  48.80 
8  48.08 
8  24.22 
8  23.28 
7  433 
7  4.30 
7  44-94 

7  4-01 

8  21.52 

7  41-30 

8  59-10 
8  58.50 
8  50.64 
8  49-53 

7  35.10 

8  37-57 

7  4l^56 
,  41.92 

8  28.75 
7  58.12 

7  59.13 

8  45^24 


I'aii'llax. 


+  o  45  36.4 
+  o  38  8.1  I 

-  o  47  53.7 
+  I  25  49.9 
H-  2  36  SI .8 
+  o  33  57.7 
+  o  40  33.9 
+  4  58  31.; 
-t-  2  18  28.6 

+  O  12  4.5 

+  4  46  35-3 

-  I  26  4.5 

+  4  38  13.'' 
t  4  7  54-9 

-  o  15  9.0 

+  I  7  55-4 

+  o  43  53.6 

+  o  36  43,3 

-  I  58  40.0 

-  5  o  36.6 
4-  o  51  18.0 
+  1  o  31.5 

-  5  4  6.1 

-  4  49  3.7 
+1  6  32.9 
+1  7  '4 .6 
+  o  43  31.2 
+  O  51  34.3 

+  O  36  32.6 

-+-  o  28  40.1 
1  1-  o  47  56,6 
4-  o  55  24,2 
-+-  4  54  8,4 
+  0  8  6,6 
4-2  8  20  I 

-  I  16  33.8 
4-  o  37  16.9 
4-  o  39  0.8 

-  o  45  6.6 

-  o  53  30.8 
+3  9  50.3 

-  5  13  51.0 
4-  o  38  5.3 
-H  o  25  26.0 

-  4  55  29.4 
4-  o  20  14.2 
4-  o  27  34.9 
+  3  35  3».6 


-  43- '9 

-  43-38 
+  43-42 
+  40.95 

-  34.76 
+  44-54 
+  44.49  ' 

-  4.52 
+  35-28 
+  43-74  . 
4-  14.18 
+  45.97 

-  17.99 

-  28.45 

-  47.36 

-  39.45 

-  42.99 

-  43.19 

-  36.37 
4-  1.70 
+  44.41 
+  44  07 
4-     3^o8 

4-    14.86 
4-  49.66 
4-  43.68  : 
4-  48.40  I 
4-  48.11   I 

-  46.33   I 

-  46.36  i 
I   +   38.83 

4-  38. 66  ! 

-  12.55 

-  38.48 
4-  42.38 
4-  40.01 

-  49.48 

-  49-54 

-  48.65 

-  48.34 
+   31-35 

-  .  5-63 

-  43.46 

-  42.57 
4-  12.18 
4-  44-OI 
+  44-07 
+  35-52 


197 

Motion 
In  <)''.oi. 


56  58.5 

57  1^9 

58  42^7 
57  5^9 
i'  0.7 
57  42.8 
57  46.4 
57     6.5 

55  20.4 

57  1-8 

58  0.3 

59  35^6 
59  35^6 

58  33-6 

59  20.0  I 

56  6.9  j 
56  49.9 

56  53-4 
54     1-8 

60  55.8 

57  52.7 

57  48.0 
60  20. 1 

60  4.2 

61  28.5 

59  >7^o 

60  17.1 
60  14. I 

58  51.1 
58  47-4 
53  56.3 

53  56.1 
56  29.5 

54  2,5 

58  .10.5 

56  30.8 
60  51,9 
60  49,8 
60  24,6 
60  20.7 

55  28.4 

59  33.8 

j      56    16. r 

j     56  17^7 

j     59  "•5 

57  17^4 
57  2KI 

60  7,6 


igS 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


(Jrecnwi 

cli  Mean 

Geocentric 

Motion  in 

Geocentric 

1 
Motion  in 

Motion 

No. 

Date. 

Time. 

Long,  of  Moon. 

o''.oi. 

Lat,  of  Moon. 

O'l.OI. 

Parallax. 

ino''.oi. 

44 

1671,  Mar.  14 

//    m    s 
8  37     0 

.3590278 

46  59  53^3 

8  44^81 

+  3  37  37^1 

„ 
+   35-24 

60    6.3 

" 

45 

"     Apr.  22 

9  29     0 

•3951389 

198  38  41.2 

7     5^02 

—     I    21     13.2 

-   37-49 

53  59-5 

46 

"          " 

10  39    0 

.4437500 

199  13     6.3 

7     5^o2 

—     I    24    15.0 

-  37-41 

53  59-2 

47 

"     May  31 

14  21     0 

.5979167 

348  27  34.7 

8  ig.36 

—    I     6  46.2 

+  43-20 

58  47-2 

48 

1672,  May  18 

IS  24  30 

.7670139 

320  33  46.2 

7  29.06 

—    I   50  16. S 

+   36-84 

55  46-1 

40 

" 

20     3  30 

■8357639 

321  25     5.9 

7  29. 86 

—    I  46     2.1 

+    37-22 

55  49-0 

50 

"     AiiR.   2 

10  18  20 

.4293982 

246  54  50.5 

7     7-97 

~   5   13  26.2 

+    0.18 

54  10.8 

51 

"     Sept.  25 

10     7  36 

•4219445 

23S    50  21. I 

7   16.61 

-   5   10  27.3 

-    4.88 

54  41-6 

52 

"     Nov.    5 

II  30    0 

.4791667 

54  52   19^4 

8  56^47 

+   4  58     1.2 

+   6.87 

60  29.8 

53 

1673,  Mar.  22 

700 

.2916667 

55  35  37-f' 

8   1 3. 06 

+   5    10  53^3 

+     0.66 

53  23.2 

54 

1674,  Aug.  23 

12  36    0 

.5250000 

54  25     9^4 

7  33^I7 

+   4  42  45.4 

-    17-43 

55  51-S 

+  0-4 

55 

" 

13  48     0 

.575ocx)o 

55     2  57.5 

7  33^71 

+  4  41   20.9 

-    17-85 

55  54.2 

56 

1675,  Jan.   II 

700 

.2916667 

III  34  22.0 

8  26.16 

-  0     6  35.2 

-  46^83 

58  57-6 

57 

.. 

8  12     0 

.3416667 

112    16    34.3 

3  26.77 

—  0  10  29.4 

-  46.87 

58  59-3 

58 

"     Jimc22 

16    0'  0 

.6666667 

90  46     2.8 

7  43^89 

+  0  56  49.6 

-   42.09 

56  24.7 

59 

" 

17  12     0 

.7166667 

91  24  43.2 

7  44^26 

+  0  53   I3.8 

-   42.15 

56  26.3 

j 

60 

167b,  I'd).  29 

10  22  57 

.4326042 

169    3  17.1 

8  38.29 

-  4  56  59.6 

--     7. So 

59  25-8 

Ci 

" 

II   20     3 

.4722570 

169  37  32.6 

8  3S.62 

-  4   57  31.9 

-     7-42 

59  26.9 

62 

"     Mar.  IS 

7  16  28 

.3031019 

47  5"    o^3 

7     5^74 

+39  51.1 

—   29.00 

54     7.0 

63 

"     Mar.  23 

13  17  20 

■553703S 

no  50  36.5 

7  32.52 

—   2     4  28. 3 

-  36-37 

55  57-5 

64 

"     June  10 

20    0    0 

■S333333 

80  13  23.4 

7     3.10 

+  0  13  46.0 

-  39-58 

54   l'-9 

65 

"          " 

22  24     0 

•9333333 

81  24  46.6 

7     8.47 

+  0     7     9.5 

-   39-62 

54   13-' 

66 

"     June  29 

II  29  59 

•479'55I 

334  57  26.9 

3     0.24 

+   5     I   25.2 

+    13-30 

57  25-3 

67a 

"     Aug.  19 

8  24     0 

.3500000 

280  17  41.7 

8  30.70 

+    I  43     7^6 

+   42.61 

59  18.2 

1 

67 

" 

1200 

. 5000000 

282  25  22.2 

8  30.52 

+    1    53  42^1 

+  41-95 

59  16.7 

-1-0.2 

1 

68 

"    Aug.  31 

1200 

. 5000000 

77  16  55^7 

7     5-8i 

+    0    10    II..,' 

-  37.71 

54  19-3 

69 

" 

14  24     0 

.6000000 

78  27  55.5 

7     6 .  02 

+  0     3  54^3 

-   37-79 

54  20.3 

+  0.0 

3 

70 

"     Sept.  26 

17  30  24 

•7294444 

64  16  57^3 

7     5^4l 

+   I     3  17-4 

-  36-91 

54  '3-5 

71 

"     Nov.    9 

5  40  55 

.2367476 

2S1  53  33.0 

8  42^3'> 

,    2  23  36.5 

+  42.34 

60     1.3 

72 

" 

6  35   19 

.2745254 

282  26  25.5 

8  41.89 

-i-    2  31    16.0 

+  42.06 

59  59,8 

73 

1677,  Mar.    g 

12   17     7 

.511S8S6 

64  39  50. S 

7   10.02 

+  0  16  32.4 

-   38. C5 

54  34-8 

1 

74 

1678,  Feb.  27 

7    21       0 

.3062500 

63  40  50.7 

7  30^25 

—   I   18  24.0 

-   38.51 

55  52-3 

75 

" 

8  33     0 

.3562500 

64   l3  21.3 

7  29.64 

—   I   21  36.7 

-   38-40 

55  50.1 

76 

"     Mar.  28 

3     0    0 

■3333333 

8431     3-1 

7  22.44 

-   3   tl    13^0 

-  31-55 

55  >6-8 

^ 

77 

"     Sept.  24 

7     f)  32 

. 2962038 

284  49  30.4 

8  24.43 

+   4  48     9^2 

+   17.43 

58  54.0 

78 

"     Oct.  29 

8  35  38 

•3580787 

37     3  53.8 

s  32.75 

-  0     0  59.9 

-   47-41 

59  20.6 

79 

1679,  ^'^f-  29 

13  3f>    0 

. 5666667 

220    9  55^3 

7  16.28 

+1     9     1.8 

+    39-25 

5446-5 

1     80 

" 

16     0    0 

.6666667 

221  ^2  42.0 

7  17.00     +   I   15  34.0 

+   39-13 

54  48.7 

*■ 

81 

"     June    4 

15     I   30 

.6260416 

30    4     4^o 

8  34.62      -  0  17  59.6 

-  46-33 

59  32-9 

82 

" 

1600 

.6666667 

30  33  54.6 

8  34.55      -  0  21     7,6 

-  46.28 

59  32-6 

83 

"     June  24 

9  51   42 

.4109028 

284  41   24.6 

8  i6.oi      +  4  57  36.9 

4-     7.89 

58     8.5 

■ 

84 

" 

10  32  29 

•4392245 

285     4  50^" 

8  16.26      +  4  57  58.9 

+      7-61 

58     9-4 

85 

1680,  Jan.   16 

9     I   21 

•3759375 

128  15  55.5 

7  55.78  1   -  4  31   28.2 

+    17-99 

56  56.7 

86 

" 

10     7     I 

.4215394 

128  52     2.9 

7  55.16      -  4  30  05.0 

+    1S.33 

56  54-9 

87 

"     Apr.    4 

10  18  22 

.4294213 

91  23  1 1. 7 

8  19.25 

-    5   14  43^4 

-     6.41 _ 

58  33-3 

88 

"    Sept.  t3 

15     0  53 

.6256134 

64  54  25.7 

8  35^38 

-   4  46  •■!9.7 

-   20.27 

59  30-0 

89 

"     Nov.    7 

7  50  43 

.3268866 

64  33  16. I 

9     9^83 

-  4  39  27.6 

-   20.47 

61   18.4 

90 

i68i,Jan.     i 

6  27  41 

.2692245 

64  53  53^2 

8   53.16      —  4  45  23.1 

-    15-37 

60  40.3 

9' 

„          .. 

7  36  41 

.3171412 

65  36  5>^3 

8  58^45      -  4  46  35^7 

1 

-    14-86 

■ 

60  41.2 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


199 


Grcuinvich  Mean 

1 
Geocentric       Motioning     Geocentric 

Motion  in 

:  Motion 

^'inll-iv                                ' 

No. 

Date.                        Time.                Long,  of  Moon. ^      C'.oi. 

i                            ' 

Lai.  of  Moon. 

o''.oi. 

(iraii.ix. 

ino''.oi.  j 

-    92 

1682,  Fell.  15        7     4  31       .2948033  1 

1 
63  27  54-5        8  21.37 

i                   1 
—  5  17  40.1      +     0.80 

58  40.! 

■■ 

93 

"     Mar.  14       9  -15  35      .4o'-655i  " 

61   48  36.0        8   14. 82      -    5    14  55.9      -     0-43 

58   13.8 

94 

10  57  35      ■45(16551 

62  29  50.4        8   15.14      -   5   14  56.7      +     0.03 

f3   15.2 

95 

i6S3,Jan.     y       8  41  32      . 3^21759 

65    19  27.0        8   1S.13      -   4  54  29.8  _   +    15-99 

58  25.3 

96 

9  54  47      .4130440 

66     I  42.3        8   19.14      -   4  53     6.5      +    16.59 

58  28.1 

97 

"     Fell.    5      II   57  42      .4984027 

61   51   25.5        7   58.01      -    5     3  33-0      +    13-24 

50  20.7  ! 

98 

12  47  44      .5331482 

62   19     7.6        7  58.66      -    5     2  46.4      +    13.63 

57    22.7            -       . 

99 

"     Aiir.    2       8  43  44      .3f'37037  , 

79  16  42.7        7  54.48      -    4     3  47-7       -1-    25. iS 

57     7-8  :       -      . 

100 

9  43  34      .4052546  ■ 

79  49  34-9        7  54-84      -  4     2     1.7      +   25.56 

57                     -      • 

lOI 

"     May     4       9  55  =3      .4134606 

145  25   17- I        3  2987      +    I  24     I.I   j   +  43-16 

59  22.3          .      . 

102 

10  40  55      .4450811   , 

145   52   10.3        S  30.05      +    I  26  17.7  1   -r  43.11 

59  22.9  1       -     . 

103 

1684,  July  12       2  16    0      .0944444  : 

no  36  32.9        7  ^5.60      +  0  20  56.7      +   43.79 

57     7-9         -     • 

104 

4  40    0      .1944445 

in   55  53-3       7  56.53      +  n  28  15. i      +  43-80 

57   n-4  '       .      . 

105 

"     Dec.  21  ■     9  24  59      -3923196 

90  28  46.8        7   21. '-8      —  0  39     6.3      +   40.50 

55     1.2          -      . 

106 

10    0  59      .4173496 

90  47   II. 0        7  21.83      -  0  37  24.8      +    40.58 

55     I. 8          .      . 

107 

l085,Oct.   17       9  29  28      .3954630 

85  44     7.8        7     3-68      +  0  26  56.1      +   37-92 

54     8.1          .     . 

108 

ifi86,  Apr.  10       93329      .39S2523  1 

230     0  25.1        8  31.42      +   I    51     9-8  ;   -   42-7S 

59  16.3          .     ■ 

log 

10  45  29      .44S2523 

230  43     2.6        8  31.63      +    I  47  35.3  i  -   42.99 

59  17.3          •     • 

no 

"     June  25       9  45  4'      .4067245  ; 

149  21   46.0        7    14-74      +58  36.7  ,   -r      7.17 

54  35.3  \       ■     • 

.  m 

"     July     2       9  13  35      .3844329  j 

240  53  20.4        8  42.11      +  0  49  10.9  ^   -   47.12 

60     1 . 9 

112 

1  1O87,  Mar.  28      13  30  37      .  56292S2 

189     6  30.7        7  27. oS      +   3  31   =2.9      -   29.07 

55   15.7          .     • 

113 

1       "     May  II        100      .0416667 

51     0  17.9        8     3.84      -  0     3  55.5      +   44.69 

57  38. I          .      . 

114 

.. 

2  12    0     .0916667 

51  40  36.1        8     3.30     -  0    0  12.1  1  +  44-63 

57  36.2          .      . 

115 

1689,  May  21 

9  29  11      .3952662 

too   17     0.4       8  40.67      +   5     7  29.9  j   +     2.94 

59  42.1 

116 

"     Sept.  13       3  20    0      .138SSS9 

171    20  55.5        7  37-78      4-    I    19  54-6  1   —  40.86 

56     1.5          -     • 

117 

4  32    0      .1888889 

171   59     3-4        7  37-31      +    1    16  30.4      -  40.87 

55  59.9  :     .    . 

IlS 

i690,Apr.  13      II   28  55      .4784143 

86     7  20.7        8  41.57      +   5   12  56.4  1   +     0.17 

59  47.8          .      . 

1     I'9 

"     July     2 

14  59    9     .6244097 

55    17  48.6        8  47.90      +   4  34  51-1      +    19.48 

60  1 1 . 0         .     . 

120 

1699,  Auk.  iS      '3  35  19      .5661921 

64   56   16.9        8  27.31      -   4  57  48.5  1   —    14-50 

59     1.6 

121 

14  13  :9      .5925S10 

65   18  35-3        3  27.53      -   4   58  26.7      -    14.33 

59     2.6         .      . 

122 

"     Sept.  22      20     0    0      .8333333 

179   10  45.4        8   18.85      +  0  33  20.3  1   4-  45-83 

58  31.4          .      . 

123 

22  24     0      .9333333 

180  33  48. 5        S   17. 88      -f  0  40  57.7  ;   +    45-59 

58   27.9   ;         .       . 

124 

I70I,Aug.23      12     0     0      .5000000 

29  51      8.5        7     9-26      -   5     2  58.4   ;   -    II-I6 

54    16. I            .       . 

125 

,. 

13  12    0     .5500000 

30  26  54.8        7     9-44      -    5     3  53.5  •■   -    10-84 

54   16.9 

12f 

"     Sept.  22 

17  50     5      •7431134 

65  49  31-4  ,     7  23. 48      -  4  49  46-9  i   +    '3-67 

55  n-9         -      - 

1 

127 

i   18  36  24      .7752778 

66  13  21.0  1     7  23.63      -   4  49     2.1   •   +    13-98 

55  13-0         -      • 

128 

1704,  July  2^        I  20    0      .0555556 

78   II   32.3  '     7   12.29      -  0  14   15. 1    ,   +    39.03 

54  36.0  -       .      . 

I2( 

2  32    0  .   .1055556 

78  47  32.8        7   '2.04      -  0  10  59-8  '   ■+-   39-02 

54  34-9          .      •  1 

131^ 

1705,  Aug.   4     >5  14  37      .63.^1505 

313   iS  20.6       9     3.10      -  4  43  34,4      —    13-65 

60  52.9 

•      • 

<3 

!       ■•     Sept.   2      II   39  35      .4858218 

334  36  37-7        9   "-Si       -   4  58  22.8  !   -f      6.23 

61   22.6 

•      • 

13; 

i7o6,Jan.  23      11     4  I4      .4612732 

64  28  16.4  ■     8     4-38      +    I    10  23.3      +    .,1.60 

57  49-6          .      . 

13: 

) 

II   40  14      .4862732 

64  48  27.7  i     8     4-20      +    1    12     7-3      +   41.53 

57  48.8          .      . 

«3- 

1         "     Jan.  27 

11   22  33      .4739931 

117     2  23.9  1     7  38. 50      +  4  35  26.8      +    15-90 

55   53-8     -0.39 

>3 

,         "     Apr.  21 

8  51  49      -3693172 

:    143  36   o.g  ;    7  18.52    +  5  12  27.8  i  -    6.32 

54  53.5          .      ■ 

•  3< 

5  ,       "          " 

9  45  24      .4065278 

;    144    3  13-2  i    7  'S-30    +  5  12    3-9    -    6-58 

54  52.4          .      ■ 

»3 

7  !      "     May  11 

20  30     0       .84; 2222 

50  15  43-5  1     8  55.10      +  0  31  40.3      -t-  49-21 

60  39.5          .      . 

13 

3  '       " 

22   44     0       .9472222 

51   44   50.3        8   54.53      +  0  39  51-9      +   48-9S 

60  37.2          .      . 

J3 

1  i      "     May  24 

10  38  30 

.4434028 

!     212  34  39-4  1     7     8-44  ,   +    ■      5  40-3  '   -   38.59 

54   >6.9  >       .      . 

14 

1 
0  j      "     Nov.  17 

II  48     5 

.4917246 

'      23  58  34-0       8  58.96     -   1     3  12.8      +  48.64 

60  56.5  ,       ■      - 

200 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Greenwich  Mean 

Geocentric 

Motion  in 

Geocentric 

Motion  in 

Motion 

No. 

Date. 

Time. 

Long,  of  Moon. 

oii.oi. 

Lat.  ol  Moon. 

O'l.OI. 

Parallax. 

ino'f.oi. 

141 

1707,  Apr.     4 

A    m     s 
8  II  52 

.3415741 

43  25  40.5 

8  56.18 

+ 

I  33  35^o 

+ 

47.32 

60  44.9 

" 

142 

"    Sept.    3 

7  37  33 

•3177431 

245  43  I6.4 

7     6.49 

- 

3  51  23.8 

_ 

25.90 

54  14.7 

143 

ii          (( 

8  25  45 

•3512153 

246     7     3.8 

7     6.42 

- 

3  52  50.3 

25.68 

54  14.6 

144 

1708,  Feb.  23 

7     8  22 

.2974769 

359  32  41 •& 

7  52.93 

- 

0  46  37-3 

+ 

42.52 

56  59-5 

145 

"    Sept.    6 

9  27     6 

•3938195 

63  53  15^7 

8  17.34 

+ 

4  46  48.5 

+ 

19.23 

58  28.1 

146 

"    Sept.  13 

6  30    0 

•2708333 

162  55  38.5 

8  38.18 

+ 

I    26  22.1 

45^98 

59  39.0 

147 

" 

8  54     0 

•3708333 

164  21  55.5 

8  37.46 

+ 

I  18  40.8 

46^31 

59  36.2 

147a 

" 

18  30    0 

•7708333 

170     5  36.7 

8  33.83 

+ 

0  47  36.2' 

- 

46.90 

59  24.2 

I47i 

20  54    0 

•8708333 

171  31     8.6 

8  32.86 

+ 

0  39  46.8 

- 

46.94 

59  20.9 

148 

i7og,  Apr.  20 

7  41     6 

.3202083 

166  46  1 1. 2 

8  34.73 

+ 

0  II     9.0 

- 

46.68 

59  33.2 

149 

"    Sept.  16 

10  40    0 

.4444444 

331     3  52.5 

7     4. So 

- 

0  51  49.8 

+ 

38.69 

54    0.8 

150 

"          " 

II  52     0 

•4944444 

33'   39  16.3 

7     4.84 

- 

0  48  36.0 

+ 

38.76 

54     o.g 

151 

"     Sept.  23 

8     9  II 

■3397106 

54  59  50.1 

7  40.33 

+ 

5     4     3^8 

+ 

11.07 

56  10.2 

+0.42 

152 

"           " 

8  57  II 

•3730439 

55  25  25.5 

7  40.55 

+ 

5     4  40.2 

+ 

10.78 

56  II.4 

153 

"     Dec.  14 

500 

•2083333 

54  30  10.7 

7  54.62 

+ 

4  57  43.4 

+ 

6.96 

56  56.0 

154 

•   7  24     0 

•3083333 

55  49  26.6 

7  56.03 

+ 

4  58  48.3 

+ 

6.02 

57     0.4 

155 

1710,  Dec.    4 

4  32  58 

. 1895602 

54  42  23.6 

7  19.78 

+ 

4  58   13.0 

6.47 

54  44^0 

156 

" 

5  44  58 

.2395602 

55  19     3.7 

7  20.14 

+ 

4  57  39-4 

6.92 

54  45^1 

+0.23 

157 

1711,  Sept.  30 

15  20    0 

.6388889 

55  35     7^9 

7     6.53 

+ 

4  35  39.9 

15.51 

54     4^8 

■'     158 

" 

17  44     0 

.738S889 

56  46  13^8 

7     6.42 

+ 

4  33     0.8 

- 

16.20 

54     4-7 

159 

1712,  May  15 

II     6  58 

.4631713 

170  24  29.7 

8     1.54 

- 

4  36  20.2 

- 

18.88 

57  32^9 

160 

" 

II  46  II 

.4904051 

170  46  21.9 

8     2. II 

- 

4  37  II. 6 

- 

18.73 

57  34^4 

161 

1713,  Dec.    I 

II  49     4 

•4924074 

68     5  59' 5 

7  46.49 

+ 

0  53  38. 8 

- 

42.47 

56  33^6 

l62 

1714,  Mar.  20 

9    6  39 

.3796180 

65  15  35^8 

7  57.47 

+ 

0  32  12.2 

- 

41^93 

57  29.7 

163 

"     Mar.  21 

10  16     9 

.427S819 

78  55  26.1 

7  J  1. 20 

- 

0  40  13.7 

- 

40.50 

56  32.6 

164 

"     Apr.     6 

15  17  21 

.6370486 

278  55  14.8 

8     7.33 

+ 

2  29  27.0 

+ 

38.01 

58     2.8 

165 

II 

16  30  36 

.6879167 

279  36  37^2 

8     7.87 

+ 

2  32  40.6 

+ 

37^82 

58     4.9 

166 

"     Sept.  27 

9    0  40 

.3754630 

61  49  47.1 

8  20.36 

- 

0     4  38.7 

_ 

44.79 

58  49^7 

167 

"     Oct.     2 

14  37  51 

.6096181 

129     8  26.9 

7  16  14 

- 

4  45     8.5 

- 

14.32 

54  43-6 

168 

1715,  May     2 

19  12     0 

.8000000 

40  47  52.7 

9     3.46 

+ 

0  51  30.0 

- 

49.54 

61     7.8 

169 

"     June  22 

200 

.0830000 

337  38  50.1 

8  16.84 

+ 

4  54  41.2 

- 

13.94 

58  23.0 

170 

"     July  21 

14  49  43 

.6178588 

9  59     6.5 

8  2g.oo 

+ 

3     4  20.6 

- 

35.77 

59  14^0 

171 

II          II 

15  42  30 

•6545139 

10  30  13.4 

8  29.08 

+ 

3     «     9.2 

- 

35^98 

59  14.3 

172 

"     July  24 

13  28  39 

.5615625 

51  34  10. 1 

8  26.88 

0  22  52.3 

- 

44^78 

59  10.4 

«73 

II 

14  14  26 

•5933565 

52     I     1.6 

8  26.81 



0  25   14.5 

- 

44.70 

59  10. I 

«74 

"    Aug.  15 

II  46  34 

.4906713 

335  28  18.4 

8  36.13 

+ 

4  41  49.5 

- 

15.78 

59  21.0 

«75 

II          II 

12  31  41 

.5220023 

335  55  16^4 

8  36.20 

+ 

4  40  59.3 

- 

16.26 

59  21.9 

176 

"    Oct.     9 

7  55  53 

•3304745 

335  21   17. 1 

8  34.69 

+ 

4  47  33.2 

- 

19.04 

59  24.3 

"77 

"     Dec.  30 

7  17  35 

•3038773 

335  58     5-1 

7  59.02 

+ 

4  32  20.1 

18.98 

57  20.4 

178 

1717,  Sept.  25 

8  53  38 

•3705787 

65     5  39-7 

8  14.12 

- 

4  36  58.0 

- 

22.10 

58  13.9 

179 

" 

9  45  58 

•4069213 

65  35  35^2 

8  14.53 

- 

4  38  17^3 

- 

21.82 

58  14.9 

180 

1718, Jan.    15 

13  24  33 

•5587153 

105     0  54.2 

9     7.74 

- 

4   49  15-7 

+ 

14.69 

61     9.9 

I8l 

"     Fel).     9 

6   22    14 

■  2654398 

65  35  40.9 

8  12.80 

- 

4  53  48.8 

- 

I5^I3 

58  12.6 

182 

"     Feb.  14 

6  50     0 

.2847222 

139  19  12.4 

9    10.12 

- 

3     4   I5^8 

+■ 

40.38 

61  25.9 

■83 

"     Sept.    9 

8  33  19 

.3564699 

347    "  19^2 

7     5-56 

- 

0     5  15.3 

- 

39  39 

5»     1.4 

184 

1719,  Apr.  22 

7  33  37 

.3150116 

66  20  37.3 

7  29.35 

- 

5     5     i^i 

+ 

0.79 

55  22.4 

185 

(1          II 

8  23     6 

•3493750 

66  46  21.3 

7  29.60 

- 

5     4  57-6 

+ 

1.08 

55  23.3 

186 

"     Aug.  21 

7  34  50 

•3158565 

231     6  30.9 

8  26.56 

+ 

5   15   17^2 

+ 

5.46 

58  59.1 

187 

'"    Oct.  5o 

8  37  27 

•  3593403 

65  12  51.8 

7  16.36 

— 

4  56  10.8 

+ 

6.91 

54  33.3 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


20 1 


lkt„ 

Date. 

Greenwich    Mean 

Geocentric 

Motion  in 

Geocentric 

Motion  in 

1 

Parallax.    ,""" 
in  c 

,j 

tion 

No, 

Time, 

Long,  of  Moon 

o''.oi. 

Lat.  of  Moon. 

0 

■".oi. 

•I  .01. 

18S 

1719,  Oct.   30 

9  33  45 

■3984375 

65  4'   W^7 

7  16.50 

-  4  55  43-1 

4- 

7-21 

54  33-9 

" 

I8y 

"     Nov.  26 

6  55  20 

,2884259 

61   14  15,9 

7  1S.70 

—  4  56    4-9 

+ 

6.15 

54  36-9 

•   i 

190 

1720,  Apr.  20 

12   15     0 

,5104167 

186  10  58.6 

3  57.19 

+   3  53  48.6 

+ 

29.71 

60  41.3      4-0.20 

191 

" 

12  43  48 

,5304167 

186  28  53,3 

8  57^37 

+   3  54  48-0 

+ 

29-57 

60  42. 1      +0.26  1 

1(32 

"     Dec.  31 

300 

,  1250000 

3"  24     1.9 

8  36.24 

—     1       2      7.0 

- 

46- 58 

59  38-3 

103 

" 

4  12     0 

,1750000 

312     7    1^7 

8  35^52 

-    I     5   59-6 

- 

46-34 

59  35-6 

I'M 

1722,  t)ec.     S 

1   30    0 

.0625000 

255  58  21,3 

8  20.94 

+  0  41   39.6 

- 

45-88 

58  38.5 

l>)S 

1724,  May   22 

5  48     0 

.2416667 

61  59  10.6 

8  56.4* 

—  0  34   1 1. 6 

+ 

49-28 

60  44,3 

igf. 

" 

700 

.29ir)667 

62  43  51,6 

8  56.18 

+   0  33   18.2 

+ 

49.20 

60  43.2 

■g? 

1725,  Fell.   19 

12   16  12 

.5112500 

60     8     2,4 

8  27.28 

+    I  44     5.5 

4- 

42.23 

59  13.0 

198 

1726,  Jan.    18 

700 

.2916667 

128     5   17.2 

9     4.72 

+   4  49  53-6 

- 

12.09 

61     0.4 

•99 

" 

8   12     0 

.3416667 

128  50  40,8 

9     4-25 

+    I  48  51-3 

- 

12,71 

60  59,0 

200 

1727,  Feb.  27 

&  52  30 

.28645S4 

53  56  22,0 

7  46^1 1 

+    4  12  43^3 

+ 

25,52 

56  41.5 

201 

"     Sept.    6 

13  4'8     0 

.5750000 

55     5     0.6 

7  <32 , 66 

4-  4  44   10,5 

+ 

18.62 

55  48.8      +0.41 

202 

15     00 

.6250<X)0 

55  42  46.4 

7  33^i7 

+   4  45  42-8 

+ 

18.23 

55   50.8      4-0,41 

203 

.. 

Ifl    12      0 

.6750000 

56  20  34. 8 

7  33-78 

+   4  47  13^2 

4- 

17.86 

55  52.7      4-0.40 

204 

1728,  Aui;.  2fl 

14    28    35 

.6031829 

55  42   16,2 

7  13.48 

+   5   14  22^2 

+ 

5-31 

54  36.5 

205 

1729,  Dec.     3 

1500 

.6250000 

56  13  57^5 

7     8.54 

+  4  47  52  6 

- 

12.28 

54     2.2 

20f) 

1733,  Mar,  22 

5  3"    55 

■2304977 

92  58     9.1 

8     4.78 

-   2  30  39,3 

- 

37-49 

57  53-8 

207 

■•     Mar.  25 

5  26  36 

.226S056 

131   59  57^7 

7  35-40 

-  4  44  169 

- 

14.56 

55  51-8 

20S 

1736,  Apr.  14 

8   18  41 

•  34f)3079 

66  28  27,9 

7  5I^42 

-  4  34     4-5 

- 

21.26 

56  47-8 

209 

"     Aug.    I 

16    13    12 

•6758334 

65  46  55-5 

7  53-76 

-  4  45     5-3 

- 

16,21 

57     3-5 

210 

17   25    14 

•7258565 

66  26  27, I 

7  54-59 

—  4  46  26.2 

- 

15-86 

57    6.2 

211 

"     Oct.    22 

12    43    39 

.5303125 

66     I   50,2 

7  35^29 

-  4  51  35-0 

- 

14.67 

55  45.9  : 

2T2 

-     " 

13    58    30 

.5S22917 

66  41    17,0 

7  35^62 

-  4  52  50.2 

- 

14.18 

55  47-4 

2.3 

1737,  May     7 

7  40  55 

,3195081 

137  52     3.5 

8     9^53 

—   2  24  48.8 

+ 

38. 3? 

58  10.9  ' 

213" 

"     May  22 

13  55   13-3 

,5800151 

349  23     3^9 

7     7^82 

-  0  23  23,4 

- 

37.77 

54  22.0 

213/. 

"     July   22 

n  34  32-' 

.4S23217 

64     4  543 

7  23-70 

-   5     8  48.5 

- 

4,01 

55     7.1 

214 

173S, Jan.      2 

4   18     0 

. 1 79 1 667 

63  21    iS,7 

7  13-91 

-   5     6  30-9 

+ 

1.60 

54  26.1 

215 

,. 

(>  42     0 

.2791667 

64  33  38,9 

7  14-41 

—    5     6   ii.o 

4- 

2.41 

54  27.8 

2I() 

9     f)    0 

.3791667 

65  46  4,4 

7   14-99 

-    5     5  42.7 

+ 

3.22 

54  29.6      +0,16 

217 

" 

II  30    0 

.4791667 

66  58  35^5 

7   15-56 

-    5     5     6-1 

4- 

4.03 

54  31-4      4-0.17 

218 

■•     Fi'h.     2 

b     8  35 

.2559607 

109  32  40,8 

7  42.06 

—   3  24   10.2 

4- 

32,26 

56  15..0 

219 

"     Auk.    S 

13     00 

.54l')W)7 

63  13     7-1 

7     7-57 

-   5     9  18.1 

-L 

8,51 

54   11.8 

220 

15  24     0 

,6416667 

64  24  21,8 

7     7^6l 

-    5     7  48.6 

+ 

9-33 

54  11. 8 

221 

.. 

20    12      0 

.8416667 

66  46  51.8 

7     7^6i 

-   5     4  25.7 

4- 

10.88 

54  1 1. 8 

222 

"     Oct.     2 

9  56  23.7 

.4141632 

65  41  42,6 

7     S.65 

-  4  54  25.3 

4- 

10.80 

54  13,1 

223 

" 

10  5&  44.3 

.4560682 

66  11   38,5 

7     8.54 

-    4  53  39-4 

4- 

11.09 

54   12.9 

224 

"     Dec,  23 

5  24  32 

.2253703 

65  27  45,8 

7     7.61 

-  4  43  45-5 

+ 

■5-23 

54     0.7 

225 

" 

'1  24  33 

.2670485 

65  57  27,1 

7     7^57 

-  4  42  41-3 

4- 

15.54 

54     0.5 

225</ 

1739,  Feb.   15 

(i  50  49 

.2852893 

59  16  41-5 

7  12.32 

-   5     I     7-4 

4- 

12.27 

54  29.9 

22f. 

"     Auk.    4 

2  3fi     0 

.1083333 

131     3   U-l 

7     8.94 

+  0  48  39.2 

4- 

39-15 

54   14-5 

227 

,. 

500 

.2083333 

132  14  46.5 

7    9-30 

+  0  55   10.9 

+ 

39-15 

54  15-8 

228 

"     Oct.    23 

II   39  40 , 0 

.4858796 

112  41  42.4 

7     4.58 

-   0  24  38.0 

4- 

37-42 

54  15-I  1 

229 

.. 

12    50  20,2 

•5349560 

U3  16  26.1 

7    4.48 

—  0  21  34.2 

4- 

37-47 

54  14.9 

230 

"      Oct.     2,( 

11      9  43,0 

..(650810 

124  14  36.1 

7     4-98 

+  0  36  32.6 

4- 

37.31 

54  16.7 

231 

^ 

12    if)      5.0 

.5111 6(jo 

124  47   15-2 

7     5-05 

4-  0  39  24.6 

+ 

37-30 

54   17-I 

232 

174(1,  Mar.  26 

800 

•3333333 

57     3  I5^9 

<     7  12.14 

+  4  43    ^-3 

4- 

17.62 

54  27.3 

=33 

1747,  Inn,    20 

1300 

,5416667 

57  22  22.3 

7     8.15 

+5     7  33-1 

4- 

5-74 

54  13-2 

234 

"     July  30 

1200 

.5000COO 

56  23  42.2 

;   7  7-93 

+   5   14  50-4 

0.02 

54   13-3 

26- 


-75  Ap.  2 


ao2 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Ohscrrotions  by  Fi.amstkeu. 

These  observations  are  used  as  printed  in  Volume  I  of  the  Jlistoria  Coclcstis 
IJiUaiinica.  His  clock  seems  to  have  been  rather  interior  'to  those  of  his  French 
contemporaries,  while  its  correction  was  less  carefully  and  regularly  determined. 
For  this  purpose  he  appears  to  have  depended  entirely  on  altitudes  of  sun  or  stars 
observed  with  a  (luadrant,  and  to  have  made  no  eft'ort  whatever  to  eliminate  })ossible 
constant  errors  by  observations  on  both  sides  of  tlie  meridian.  To  this  we  have  to 
add  the  fact  that  typographical  errors  in  the  Histori'i  Coclcstis  are  so  numerous  that 
uncertainties  frequently  arise  from  them.  It  is  therefore  hardly  possible  to  form  a 
judgment  of  the  probable  errors  of  the  dock-corrections. 

It  does  not  appear  necessary  t<>  reprint  the  observations  in  full;   but  we  pi-esent 
the  clock-errors  resulting  from  the  individual  altitudes  in  the  following  table : — 
Imiivii/iial  Corrections  to  Flamstcar s  Clock,  irs  s^hrii  h  Altitudes, 


Dale. 

Greenwich 
Mean  Time 

Coriec- 
tion.       ' 

I! 

'"      '    i 

+  12  4 ; 

Date. 

Gicenwich 
Muan  Time. 

("orrec-   , 
lion.      i 

tn     s 

+     4  28 

Dale. 
1682,  Mar.  II 

Creenwich 
Mean  Time. 

h    HI     f 
21   30    4 

1 

Correc- 
tion. 

1676,  Mar.  18 

/;    m     s 
7  41   34 

1676,  .\ug.  30 

20    12    2b 

1 
m     s 

-     5  3" 

44   II 

12  I 

1336 

4  2O 

33    0 

5  3" 

• 

47  41 

12     6 

14  45 

4  30  : 

35  54 

5  24 

Mar.  22 

49  54 
10  13  5') 

12     4 
+      4    12 

Nov.    y 

f,  4f,  51. 
51    KJ 

-    3  40  1 

3    42    : 

Mar.  14 

II     0  37 

2  23 

-      5  42 
5  42 

17   18 
20  43 

3511 

3  56  1 

53  3' 

1 

3  41 

■ 

4  25 
6  32 

5  43 
5  44 

23   10 

3  58  ' 

1677,  Mar.    (J 

7  50  41 

—     0  22 

1O83,  Fell.     3 

6  13  24 

-      I    52 

II  17  ly 

3  47  j 

51   56 

0  23 

"5  34 

I   54 

Mar.  24 

7  57  38 

8  7  29 

+     4   18 
4   14 

53   "3 

55  47 

0  25 
0  25 

Fell.     5 

17  44 
9     5  4fi 

I   51 

-      2     4| 

8   17   12 

4  27 

Mar.  It 

7  20 

-     0     7 

7  54 

2    4' 

June  26 
30 

5     0  23 
28  4<; 
48  28 

5  2O  30 
31   22 

+     fj   II 
6  16 
6  20 

+     8  47 
8  46 

I&7S,  Oct.  28 

7    "2  43 

K)    12 
22    27 

2S    58 

i   -      5   51 
'           5   52 
5  4^ 
:          5  54 

Apr.     I 

10      1) 

12  27 

14  48 

20   17   15 

19  33 

2    4 
2     3  j 
2     4  ! 

-     5  50  i 
5  53 

1 

Aug.  19 

3  3fi     ') 
33  27 

+      5  43 
5  44 

•            Oct,   29 

II   25     5 
28  22 

-     6   II 

1  -  ''  " 

fi 

21   53 
20  40 

5  52! 
-     551 

43     3 

5  48 

1O80,  Jan.   1(1* 

7  22     0 

+  II  16 

30 

20     5 

-     6     I 

20  25     8 

+      5  23 

27  15 

II 23 

M.ay     6 

19  45 

-      5   59 

28  33 
3U  51 

5   19 
5   15 

' 

31     8 
34  45 

.125 
j     II 23 

1686,  \\ix.    g 

20    20 

-     S  34 

35  31 

5    18 

. 

38     9 

i  +  II  21 

20 

20 

-    12  52 

1676,  June  o,  29.1 
I,    5-6 


*  Clock  losing  alioul  32"  per  day  on  mean  lime 

Clock-com'ctions  for  Fla.mstkeu's  Ed'qms. 

-2    lo'     1 684,  July   8,      5—4  28      1689, 

-I   46  12,      5    —  3  40 

1687,  May   6,  20.0  —12  25 

1687,  May  II,   4-5—14  30 


Sept.   5,    1.8  -f-i   29 

Sept.  12,    3.9  -f-i  49 

20.0  -\-2     5 


RESEARCHES  ON  TIIK  MOTION  OF  THE  MOON. 


203 


Lonf^liidcs  and  Latitudes  of  Stars  for   1850. 
Adoplfil  <)lilii|uity  for  1850,  23°  27'  3i".4. 




' 

Name  of  star. 

Lon«.,  1S50. 

1 

/,' 

/'I 

Lat.,  i"-o.      j 

i 

B 

B" 

/'J 

t 

i 

iS      Pisciimi        .... 

12     3     4.!>f> 

5027.30 

+     3-75 

1 
+   2   to  24.00 

+     7-77 

+  0.17 

1 

--  7  -  33 

"      Pisciuiii        .... 

25  3S  41 .  10 

5030.82 

+     4-45 

-    I    37  54-1' 

+    '7-45 

+  0.14 

-      7-7' 

I.alandc  4903   . 

/)'    Arietis 

44  4f)  28.02 

5044.77 

+   20.13 

+    I    10  34.52 

+     0-95 

-4-  o.oS 

-    26. 88 

B.  A. C.  020     ..     . 

t      Ariclis 

46  24   11).  J2 

5021.50 

-      1-50 

+    4     9  3l-fi5 

+   37-45 

+  0.08 

—     o.lS 

(i      Arirlis 

48  45   "0.1)5 

5037.80 

-+-   13-40 

+    I   48  35-3» 

+   35-01 

+  0.07 

-      3-75 

Ariflis 

49  51      '-50 

5018.76 

-     5-17 

+   2  52  40.60 

+   3'-99 

+  0.07 

-      7-27 

/     Taiiii 

51   20  47-81 

5028.22 

+     0.40 

-    5   55  55-7f' 

+   39-62 

-\-  0.06 

-     0.37 

1)      Taini 

55  20  44.37 

5020.02 

-     2.80 

+   3  42  22.55 

+   35-94 

+  0.05 

-      5.62 

16 

,(,r      PIciadiim  (Cclaeno)   . 

57  20  27.90 

5023 . 46 

—     0.21 

+   4  20  58.47 

+   36.30 

+  0.04 

—     6,01 

17 

//      I'luiadum  (Elcclral     . 

57   li)  04.12 

5023.52 

—     0.21 

+-   4   10  27.23 

+   36-29 

+  0.04 

-     6.01 

m     f'leiadiim    .... 

57  32  3f'.3f' 

5023.20 

—     0.20 

+   4  52     3.00 

+   36-37 

+  0.04 

—     6.01 

i  '9 

(•      Pleiadum  (Taygita)    . 

57  28   14.20 

5023.42 

—     0.20 

+   4  30     0-03 

+   36.34 

+  0.04 

—     6.01 

20 

c       PIfiaduin  (Maia)   . 

57  35   10.4S 

5023.47 

—      0.20 

+    4   22   27.82 

+   36-38 

■  1-  0.04 

—     6.01 

,  23 

(1      Pleiadum  (Meroiie)    . 

57  36   18.62 

5023.63 

—      0.20 

+    3   56   24.61 

+-   36-38 

•)-  0.04 

-     6.02 

7     Tauri 

57  53  53-58 

5023.62 

—     o.ig 

+   4     2     6-9) 

+   36-49 

+   0.04 

—     6.02 

27 

/     Pleiadiini  (Atlas)  .      . 

5S   15  42.32 

5023.61 

-     0.17 

+   3  54     6-42 

+   36.61 

+  0.04 

—     6.03 

/(      Plfiadiini    .      .      .      . 

58    17     6.70 

5023.68 

-     0.17 

+   3  58  55-08 

-i~   36.61 

+  0.04 

-     6.03 

33    Tauri 

51)  51     0. 18 

5030.00 

+     5-<>3 

+  2  30  45-27 

+   39-93 

+  0.03 

-      3-25 

A'    Tauri 

fit   21  28.80 

5032.66 

+     7-80 

+   I   14  40.04 

^    33-68 

+  0.03 

-     008 

53    Tauri 

64  33  37-15 

50^7.41 

+     2 .  00 

—    0    !■     56.08 

+   38-81 

4-  0.01 

-      5-77 

u-    Tauri 

f)3  58    0.04 

5010.68 

-     5-7; 

-  0  46     3-73 

4-  40-10 

+    0.02 

-     4-32 

51    Tauri 

fi4  23  28  flQ 

5033-50 

+     8.40 

+  0  10  23.27 

+   3S-34 

+    0.02 

—     6.20 

)      Tauri 

63  42  22.34 

5038.67 

+    11.24 

-    5  44  56-14 

+   39  53 

+    0.02 

-     4-Sl 

56    Tauri 

64   42    2f).(lO 

5026.36 

+     1 .20 

+   0  18  57.33 

+   38-50 

+    0.01 

—     6.12 

58    Tauri 

f>3  -18  36.36 

5038.00 

+    11.02 

-   6  18  24. oS 

+   39- '7 

■t-    0.02 

.-      5-21 

V      Tauri 

fif)     1   17.00 

5027,84 

+     3-5S 

+40  13.10 

+  40-55 

4-  0.01 

-     4-30 

»'     Tauri 

66     6  22.07 

5032 . 00 

+     7-81 

+   0  36  38.01 

+   37. .66 

4-    O.OI 

-      7-3' 

^-     Tauri 

66     6     6.55 

5035.08 

+    10. 87 

-1-   0  30  50-01 

4-    36.87 

+   0.01 

—      8.00 

70    Tauri 

65     S  54.07 

5034-35 

+     7-f>5 

-    5  40  14  05 

+    40.8c 

+   0.01 

-      3-92 

71    Tauri      .... 

65   ifi     0-35 

5036.06 

■\      0-28 

-   6     I     2.85 

■*■   39-5' 

4-  0.01 

-      5-24 

H.  A.  C.  1373    •      • 

66  36  10.67 

5035  40 

4-    10.21 

-  0     0     4-80 

+  36- 5f 

4-  0.01 

-      8. 52 

1 

f      Tauri      .... 

66  21   58.47 

5035.6, 

+      0-78 

-    2  35      1-21 

+   3? -7-1 

+  0.01 

-     6.10 

(ii     Tauri      .... 

65   51   22.57 

5035 -30 

+      S.72 

-   5  45  43-06 

+  ;o-4. 

S       4-   0.01 

-      1-48 

If-     Tauri     .... 

65  5"   46. '3 

5036.73 

+    10.04 

-    5   51    '0-42 

+  40.7 

+    0.01 

-     4- '6 

a  A.c.  1341  •    ■ 

66  21    57.30 

5033.81 

t-       7-22 

—    5  36  22.08 

+  39-9 

5      4-  0.01 

—      5.10 

(I      Tauri     .... 

67  41   34.13 

•5020.58 

+       3-12 

—   5  28  40.80 

+  25.4 

5           0.00 

-    10.88 

i 

r      Tauri      .... 

70     3  34.50 

5024.60 

—      0.51 

+  0  41  43-Si 

-t-  42-7 

2            0.00 

-     3->o' 

(1      Tauri           ... 

So  24     6.36 

5026.21 

+     o.oi 

—    1   18  30-46 

+  45-2 

5      -  0.04 

-      1-77 

Ill)  Tauri      .... 

St    18     3.38 

5026.47 

+     1. 00 

-  4  42   10- '5 

+  46-4 

I      —  0.04 

—     0.64 

120  Tauri      .... 

81   36  38. 28 

5026.22 

-4-     0.86 

—   4  46  26. 7f 

+  47-4 

4    :     -    0.04 

-+-     0.37 

13(1  Tauri     .... 

86  25  24.56 

5016.52 

+      l.io 

+49  44-95 

+  46.0 

2    '    —    0.06 

—     I .00  i 

i 

X^    Orionis  .... 

.   '     86  42  50-3> 

5024.11 

1  -    o.gs 

-   3  42   I3-3-) 

+   44-f 

5    :    —   0.06 

—      2.36  : 

U     Geminorum      .      . 

88  51     7-05 

5025. 18 

—    0.06 

—  0  II    I5.8f 

)      -f   36-f 

6       —   0.07 

—    10.21 

3      Geminorum 

go     8  36.04 

5025.07 

1  -    0.14 

-  0   10  34-4 

+  45-' 

4      -  0-07 

-      1-7' 

Lalande  12148 



• 

1 

1 

■   1 

i 

204 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Longitudes  and  Latitudes  of  Stars  for  1850 — Continued. 


/' 

Name  of  star. 

Long.,  1850. 

/' 

/'I 

Lat.,  1850. 

/r 

B" 

— 

11-97 

Gemiiioriim 

93  12  18.48 

5032.00 

+ 

6.88 

-  0  50    5.32 

+ 

34-42 

—  0.08 

V 

Gotiiiiioruni 

QI   20  40. ql 

5019-48 

- 

5.66 

-  0  54  24.95 

+ 

44-98 

—  0.07 

- 

1.65 

V 

Ceminonim 
Weisso  II,  lf)5f) 

94  -12  30-93 

5023.30 

1.44 

-   3     4  29.55 

+ 

43-96 

—  0.09 

" 

2.20 

>. 

Oi'iiiiiioriim 

lof)  41    13.63 

5019.62 

- 

3-74 

-   5  39     4-(io 

+ 

37-54 

—  0.09 

"" 

5.69 

/ 

Oeminoiiiin 

III   34  53.38 

5022.17 

- 

I.6i 

-  3  45  40-4' 

+ 

41-94 

-  0.14 

-1- 

0-45 

s 

Geminoriim 

.    112    5q   52. (J2 

5017-39 

- 

f'.77 

-  2  39  43.70 

+ 

33-82 

-  0.14 

- 

7.10 

85 

Gemiiionim 

114    57    20.30 

5022.61 

- 

2.24 

-  0  53  44.84 

■+■ 

36-24 

-  0.14 

- 

3-87 

A 

Cancri    . 

119  43   15-34 

5026.29 

- 

1.08 

+   4  21   55.07 

+ 

33-19 

—  0. 16 

4-72 

it 

Cancri    . 

126  37  33-12 

5029.15 

4- 

3. 87 

+04  20.97 

+ 

11.19 

-  0.17 

23.09 

a 

Cancri    . 

131  32  49.20 

5026.07 

+ 

3-82 

-    5     5  32-66 

+ 

28.29 

—  0. 18 

- 

3-12 

K 

Cancri    . 

134     4  34-9<J 

5020.48 

- 

1.20 

-    5  34  54-38 

+ 

29 .  06 

-  0.18 

- 

0.77 

i 

l.c'onis   . 

139  33  22.76 

5015-35 

- 

7-73 

-   3     9  42-60 

+ 

15-07 

—  0. 19 

- 

11.11 

0 

Lt'onis   . 

142     9  32.41 

50C9.35 

- 

13-24 

-   3  45  49-64 

+ 

16.07 

-  0.19 

- 

8.31 

n 

Leon  is   , 

145  48  34.08 
147  44  39-90 

5027.87 
5001.63 

_ 

0.92 
23 -95 

-f   4  51   25.06 
+  0  27  35.91 

+ 

21.42 
11-37 

—  0. 19 

—  0.20 



0-35 
8. 98 

Leonis   . 

- 

- 

B.  A.  C.  357'}   • 

151  31   38.50 

5021.65 

- 

7.00 

4-  4  27  58.41 

+ 

12.73 

—  0.20 

- 

4.79 

r 

Leonis   . 

169  25     0.41 

5025-93 

+ 

1.24 

—  0  33  20. 10 

+ 

1-45 

—  0.20 

- 

1  78 ! 

I  ,  jtj   1 

e' 

Leonis   . 

172  lO  59.92 

1S8     4     4-71 

5022. 17 
4974-25 

-+- 

I   63 
53-22 

-   5  42  12.52 
-1-   2  48   15.20 

+ 

0.33 
35-46 

—  0. 20 



0.57 
23.50  j 

r 

Virginis 

-  0.17 

- 

a 

Virginis      .     . 

201  44   55.24 

5020.21 

- 

3-55 

-   2     2  35.62 

- 

27-94 

-  0.15 

- 

5-54 ; 

?. 

Virginis 

214  51   31.61 

5022.20 

- 

3-35 

+  0  30  10.41 

- 

30. 89 

—  0. 11 

+ 

0-30  i 

ni 

Lilirx     . 

222    56      3.05 

5015.02 

- 

10.42 

+  0  22  51.99 

- 

47-68 

—  0.09 

- 

11-83  1 

n« 

Libric     . 

222    59    29.42 

5016.06 

- 

9-37 

+  0  21     7.60 

- 

47-08 

—  0.09 

- 

11.22   j 

>■ 

Libra!     . 

233      2    25.27 

5033.81 

+ 

6.74 

+  4  24     7.06 

- 

39.21 

—  0.06 

4- 

1-42 

!r 

Scorpii  . 

240    50   46.83 

5022.08 

- 

'-44 

—   5  27  21 .05 

- 

43.53 

—  0.03 

- 

5-04  ; 

/3' 

Scorpii  . 

241     5  43.84 

5025.33 

- 

0.23 

+    I     I   36.85 

- 

47.50 

—  0.03 

- 

3-93  1 

B.  A.  C.  5395    • 

243  17   ig.io 

5013.38 

- 

11.81 

—  0  11     6.60 

- 

43-51 

—  0.02 

+ 

0.70  , 

1         .) 

Scorpii  . 
Sagittarii     . 

249  21  47.33 

5024.37 

-r- 

0-55 

—  6     6     1.12 

49  99 

0.00 

— 

4-30  , 

Sagitlarii     . 

281  21    19.59 

5027.25 

+- 

2-44 

-1-    I   40  49.86 

- 

47-20 

-1-  0. 11 

- 

2.41   : 

0 

S.igiltarii-    . 

282  53  48.46 

5030.00 

+ 

5.00 

-+-  0  52  52.20 

- 

51-68 

+-    O.ll    .    - 

7-30  ^ 

TT 

Sagitlarii     .      . 

284    9  28.01 

5022.53 

- 

2.28 

+   I  27  24.42 

- 

47-84 

+  o.n      - 

3-83  : 

p' 

Sagittarii     .      . 

2?7    21    25.77 

5020.22 

- 

3-f'O 

-(-  4  14  26.80 

- 

42-93 

+  0. 12  i  + 

0.08  ; 

/!'• 

Sagittarii     . 

287   19  4''-l'>3 

5032. 85 

+ 

8.87 

+   3  47     '-6o 

- 

54-20 

+  0. 12     — 

U.17 

33 

Capricorni  . 

314  46  35.20 

5022. 12 

- 

f>.54 

-    5   18  38.24 

- 

41.79 

+  0.18  , 

- 

12.41 

) 

Capricorni  . 

319  41    18.20 

5043-47 

+ 

16.61 

-   2  32  35.89 

- 

30.24 

+  0. 19 

- 

4." 

(^ 

Aijuarii 

328  23  27.70 

5030.25 

-+- 

4.81   1 

-  0  16  28. f5 

- 

21.39 

+  0.20 

- 

1-49  ' 

« 

Aipiarii 

333  17  36-95 

5023.39 

- 

2.79  1 

'-    I    13   13.67 

- 

18.11 

-1-0.20     — 

1-94  1 

K 

A(|uarii 

337  19  40-03 

5010.35 

- 

n.63 

+47     8.56 

- 

21  .64 

-1-  0.20     — 

8. 62  i 

r' 

Afjuarii 

336  30     1.80 

5026.35 

- 

3-35 

-   5  39  28.56 

- 

17-55    i 

■1-  0  20     — 

3-88 ; 

H.  A.  C.  81S4   .      . 

349     7     9-75 

5035-12 

+ 

8.95  j 

-    I     7  49-10 

— 

33-16 

+  0.20 

— 

28.66 

NoTF..— These  positions  of  the  occulted  stars  are  derived   from 
standard  catalogues  are  ruduced   to  the  e<iuinox  of  my  paper  Oii  t/t, 
S/iirs  (iSjT),  and  m  which  tlie  positions  of  most  of  the  stars  observed 
of  Bkadi.i-y's  observations. 


an  unpublished  discussion,  in  whicli  lliu  severid 
*  Rit^ht  AsC'Hsions  of  the  lu/tiittoriii/  /•'iini/nnh'nt,jl 
by  llRAiil.KV  are  from  Dr.  Auwkks's  re-reduction 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Di'tnils  of  Rpihtdmi  of  tlir  Orcnlfatioiis. 


205 


Tlioso  Jire  pnN.i'nted  in  the  t'ollowiiifi'  tables  in  such  fnrni  as  to  ^ivc  as  uroat 
tiicility  as  ajJiKiared  i)ractical)le  tn  any  one  desiriiifi'  t«i  rc-i-xaniinc  and  corroct  the 
work.  Kacli  observed  occ.ultatioii  is  niunbered,  so  as  to  facilitate  siibse(|iieiit  ri't'er- 
ence;  the  arranf^enient  is  not,  however,  chron(dof>ical.  excejit  throu^ii  each  series. 
The  ditl'erent  .series  are  arranjied  in  the  order  of  tlieir  computation,  as  it  did  1  it 
seem  neee.ssary  to  run  a  risk  of  coid'usion  in  seeking'  to  make  them  more  nearly 
clironolof^ical.  'i'he  onlv  serious  displacement  occurs  in  the  case  of  Flamstkeo's 
observations,  which,  in  strictness,  should  inmiediately  follow  those  of  lli;vr,i. us.  The 
followin<>'  are  the  only  i)arts  of  the  tabh-  which  .seem  to  need  explanati(  n. 

The  data  for  local  and  (Ireenwich  mean  times  have  been  already  pretty  fully 
o'iven,  and,  in  most  cases,  the  results  are  ^iven  in  precedinj;'  sections,  and  are  here 
simply  copied  from  them.  Small  discn^pancies  may  be  found  in  souh;  cases,  as  the 
definitive  discnssi<in  was  not  completed  till  after  a  j;reat  deal  of  the  computation  of  the 
fidlowing  tables  was  made.  Any  corrections  thus  required  can  be  readily  made  in 
the  equations. 

The  sidereal  times  are  in  all  cases  from  the  mean  equinox  of  the  date,  nutation 

being-  omitted. 

The  e(dunm  "Moon's  Tabidar  Geocentric  Positiou"  gives  the  lonj-itiule  and  latitude 
of  the  moon  as  derived  from  Hansen's  tables,  and  printed  on  pages  197  to  201. 
The  lono'itude  is  counted  from  the  nu-an  equinox  of  the  <late,  as  in  the  case  of  the 

sidereal  time. 

The  ajjpareiit  tabnlar  i)Osition  of  the  moon's  centre  as  seen  from  the  place  of 
observation  is  then  deduced  from  the  geocentric  [K)sition  l)y  the  method  described  in 
§  6.  The  upi)er  line  of  each  pair  gives  the  longitude  and  latitude  of  the  moon;  the 
lower  one,  those  of  the  star.  The  latter  have  been  derived  from  the  positions  of  tlu^ 
stars  just  given  by  reducing  tliem  to  the  date,  and  correcting  for  aberration. 

Next  we  find  the  tabidar  ditierences  of  apjjarent  longitude  and  latitude  of  the 
nioon  and  star,  formed  by  subtraction  from  tlu-  two  preceding  columns. 

In  the  next  column  we  have,  in  the  upper  line  of  each  pair,  the  apparent  semi- 
diameter  of  the  moon  as  seen  from  the  place  of  observation,  using  (_)udemans's  ^  alne 
of  the  ratio  of  the  diameter  of  the  moon  to  that  of  the  earth.  The  lower  line  gives 
the  tabular  distance  of  the  centre  of  the  moon  from  the  star,  deduced  from  the  num- 
bers of  the  preceding  colunni.  If  the  observations  and  all  the  elements  of  reduction 
were  correct,  these  two  numbers  should  be  identical.  The  exi)ression  of  the  ditfer- 
ence  in  terms  of  the  elements  which  the  observations  will  enable  us  to  correct  is  the 
work  of  the  following  section. 

The  last  column  gives,  in  the  njiper  line  of  each  pair,  the  longitude  of  tlie  sun  at 
the  time  of  the  observation,  and,  in  the  lower  line,  the  elongation  of  the  star  east  of 
tlie  sun.  The  latter  mnnber  affords  the  argument  for  taking  out  the  alxa'ration  of  the 
star  from  the  proper  table,  and  tor  determining  whether  the  phenomenon  was  observed 
at  the  bright  or  the  dark  limb  of  the  moon. 


2o6 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Tabular  Exhibit  of  Reduction  of  the  Occultations. 


OCCULTATIONS  OBSERVED  HY  HULI.I ALDUS. 


;no. 


•Slar  occulteil. 
1 1'lncc  of  ol)S.] 


T  !  "  Leon  is  . 

I  Lmidon.] 

)/  Taiiri,  L 
I  Loudon.) 

r  Taiiii,  \. 
[Paris.] 

t'  Tauri,  L 
[Paris.] 


Dalr.  4  - 


lf)27, 

Innc  17 

Dec.  30 

i63'>    \ 
Apr.  7  ■ 

1641,    I 
Apr.  13  j 


Apparent   Position  of 
Moon  ami  Slar. 


Longitudes,      Latitudes. 


/■-/. 


M4     7   "S.d!    +1-^  34  25-8 
4-0  27     ij.S 


5  44     4  5  43  44       54  =4  14-8 

o  20  33'  .      .      .  I   +4  4fi  35-2 

0-  0  42  I  q    o  21 '     67  33  17.7 

to  13  13'  .      .      .  !  +1     7  55.4 

8  "3    4|  3     3  43 

9  42     7  .      . 


144  39  4-1 

54  44  5f)-'' 

54  54  12.5 

66  50  19.4!    +0  36     9.7   —  99S.3 

67  6  57.7      +0  40  13.4   -   243.7 

63  13  57.0  I    —2.28  30.91—   764.7 

63  26  41.7 


+  4  12   I5-<)  -   555-9 
+  4     o  49-7   +   fi85-3 


-2  36  23.0  +   472. 


.S" 
J} 


938 .4 

960.6 

8S1.5 

922.5 
1028.6 

838.2 
898.0 


© 

/.-0 


86.3 

58.4 
279.2 
'35.7 
17.8 
49-3 
24.1 
39-3 


GASSENDUS. 


a  Leonis,  I.    . 
[Digne.] 

;   Saeitlarii,  L 
[Digne.J 

Mars,  \.     .      .      . 
[Paris.] 

j  Mars,  E.    . 

;   Capricorni,  \.  . 
[Digne.] 

Pl.Electra,(/')L 
[Aix.] 

PI.  Mal;„  {c)  I.     . 
r^l.Merope,  (-OL 


13  !  1/  Tauri,  I. 


PI.  Merope,  L 
jAix.l 


"5 


'/  Tauri,  I, 
[.\ix.] 

/i  Geniinorum,  L 
[Digne,] 


1627, 

I  June  17 
1 

1627, 

Sept.  18 

1632, 
Feb.   5 

1632, 
Feb.  5 

1635, 
Aug.  26 

1637, 

Mar.  29 

I 

:  1637, 

'  M  ar.  29 

i    1637. 
I  Mar.  29 

;     '637. 
Mar.  29 

1638, 
Jan.  24 

1638. 
Jan.  24 

.    1638, 
I  Dec.  20 


10  30 
16  13 

10  54 
22  44 

15   i3 
12  21 

15  47 
12  50 


10     5     3 


10  29  20 


15     9  >8 


144 

50 

9 

0 

+  1 

25 

40 

8 

278  37 

23 

8 

+  2 

26 

51 

8 

15    15  37  54 
9      .      .      . 


*q  47  49 

9  22  52 

20  7  14 

8  48  58 

8  27  II 

9  '8  49 

9   22 
9   52 

9  J2 
10      2 

9  48 
10  18 

7  39 

3  55 

8  35 

4  51 

16  36 
10  35 


47  I  9     I     o 

43  :   .     .      . 

I 

21     9  10  34 

30 


9  27     7 


7  17  47! 

I 


10  ,  8  13  23 

42  i    .  .      . 

34   16  II  37 

29:   ,  .      . 


136  30  12.4 

+  4  58   18.5 

136  46  3.2 1 

+  4  58  9-5 

316  30  0.9 

—  I   26  9.6 

54  54  41 -I 
+  4  38  53-2 

55  14  58.4 
+  4  38   II. o 

'55  20  43.7 
+  4  37  59.0 

55  30  38.3 
+4  37  38.3 

54  34     5-4 
+  4     7  54-3 

55  06  05.6 
+  4     <■'     4-9 

90  40  36.3 
— o  15  22.0 


144  24  50.8  I 
144  39    41 

277  59  43-8  I 

278  15   14.9 j 

136    14    12.2  1 
136   23   41.2 

136  27   35.81 
136  23   25.3' 

316   20  44.7 

316  41  32. 3| 

54     3   10.4 
54  20  46.7 

54  23  15,0 

54  36  53-2 

5429  6.2 

54  38  I.I 

54  39  20-2; 
54  55  36-2! 

54  23     5-6 
54  39     3-9 

54  45  30-0 i 
54  S*)  38.9: 
90  00  48. o 
90  15  45.2 


+0  34  51.0 
+0  27     9.7 

+  1  46  48.4 
I  42  319 
+4  20  32,8 
+  4  33  30.6 
+  4  18  16.0 
+  4  33  30.6 

—  2  19  36.7 
—2  31  30.2 

+  4  13  45,8 
+  4     9  II-2 

4-4  10  34.3 
+  4  21   II. 6 

+  4     9  37-1 

+  3  55     8.4 

+  4     7  58.6 
+  4     o  50.5 

+  3  49   '2-9 

+  3  55     9-1 

+  3  48  54-3 
+4    o  51.2 

-o  47  19-5 

-o  51   18.4 


-  853. 
+   4f'l- 

-  931. 
+  256. 

-  5fi9- 

-  777- 

4-   250. 

-  914- 

-  887. 
4-  713- 
-1056, 
+   274. 

-  8l8. 

-  f>37. 

-  534. 
+  868, 

-  97f). 
4-  428, 

-  958 

-  356 

-  668 

-  716 

-  897 
4-   238 


3     935 '4 
3     970.0 

1  903.0 

5  965.4 

o    945.1 
8  '  962 . 6 

5;  944.3 

6  948.0 

6     982.3 

5  11138.3 

3  I  979.6 

6  1088.6 

2  '.  978.0 

3  11035.4 
977.6 

1019.4 

976.8 
1063.6 


.3 


86.3 

58.4 

'75.6 
102,7 

316.6 
179.8 


'53-3 
163, 

9.4 
45- 


9.4 

45-5 


973 .3  304.9 
109.7 


2  i 1020. 3 

9  I  972.6 
9^  979-4 

.2!  979.2 
9  ■  928.4 


304.9 
iiio.o 
i 
269.0 

181.7 


I 


*This  local  time  should  be  increased  by  2'"  23".     See  page  82. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Tabular  Exhibit  of  Reduction  of  the  Occultalious—Q.ovAmx^A., 


207 


HEVELIUS  AT  DANTZIG. 

1 
1 

No.        Star  occulted.; 

Date. 

Local  Mean  and 
Sidereal  Times. 

Greenwich  Mean 
Time. 

1 

M 

J  .a     •           Apparent  Position  of 
rt   I   0                  Moon  and  Star. 

i 

i 

/.■-Ji 

-  993-2  I 

-  401.9  I 

1 

S' 
D 

© 
/-©, 

a   Z   °            

s                   Loriv  iludes. 

S 

Latitudes. 

i 
1 

17      «  Tauri,  I. 

1644. 
Nov,  14 

1 
h    m     s    h    III    s 
14  50    9  '3  35  33 
6  28  51     .     •      • 

64  59  57-9 i     64  33  28.8 
-5    0  50.5'     64  50    2.0 

-5  36  ■4-f' 
-5  2Q  32.7 

009.0  233.0 

066.3  191. 8 

1             i 

18     a  Tauri,  E.    .     . 

I'i44. 
Nov.  14 

15   50  39|l 

7  29  31 : 

4  3f'     3 

<')5  38     3.4'     fi5     4  39-"!   -5  3f'  32-5 
-5     "  43-5       f'4  5"     2.0     -5  29  32.7 

f-   ,S77. 0:1007.4     .      .   j 
-  419.8!  967.8     .      . 

1               '             ' 

19     11  Tauri,  I. 

1645, 
Oct.    8 

1 
13  33     ()'i2  18  30J 

2  44  4f>     •      ■      -1 

f>4  27  23.1       f'4  33  49-9     -5  31   39-5 
-4  51   50.4       fi4  50  40-4     -5  29  31-3 

— I0I0.5 

-   128.2  I 

1 

995-5  195-8  | 
013.7  22q.O  i 

20     n  Tauri,  E.     . 

if>45, 
Oct.    S 

14  43     0  '3  28  44 
3  54  51      -      •      •  I 

<>5     9  57-4       ''5     (>  45-1     -5  27   53-" 
-4  5"  37-9       f'4  5"  AO.'\\   -5  29  31-3 

+  964 -7 
-     98.3 

996.2     .      .    ' 
965.2     .     .  ! 

21      H.  A.  C.  920  .      . 

1656, 
Mar.   I 

8  34  45 
7   15  3f' 

7  20     () 

44     7   19-2       43  25  48.1      -+-4  26  39-9 
-h4  54     8.1 

931.4  341.6 

.     .  1  62 

i 

22      53  Tauri,  1.     .     . 

1 

1058, 
Oct.  14 

II     6  55 
0  41   15' 

9  52  19 

61   25  40.1       61  42   17-8;   -0  30     3-0 
+  0     8     f).o       f)I   53  43-8     -0  19  II. 0 

—  68fi.o| 

-  652.0  ; 

893.0 '202. 5 
946.4  219.4 

23     ,j  Scorpii,  E.  . 

1660, 
Apr.  26 

14  38  37' 
17     I  22 

13  24     I 

238  38  45.5     23s  4"  1 1 -4     -f  I    II   54-5 
+  2     8  20.5     238  27   14.5     +1     3     <•■- 

+  77f'-9 

+  527-8 

964.3    37.0  j 
939.2  201.4 

24     (I  Virgiuis,  1. 

1660, 
June  17 

to  56  25 
16  43  35 

9  41   49 

199    0  33.4     19S  54   19-0     -2  11  23.9 
-I    If)  33.4     199     (>  31-7     -2     I  43-8 

-  732.7 

—  580.1 

927.7  1  87.0 
934-4  112. I   i 

25      71  Tauri,  1.     .      . 

1&63, 
Mar.  14 

9  39  25 
9     8  57 

8  24  49 

03     S  12.9      62  26  29.5     -5   51     7-f> 
—  5   14     0.6       O2  39  18.3     -f'     2  20.5 

-  768. 8 
+  672.9 

9S0.4  354.0 

1018.5     07.1   1 

1             j 

26     W  Tauri,  1.      .      . 

1663, 
Mar.  14 

10  32     7 
10     I  48 

9  17  3" 

O3  39  46. f.      fi2  5f'  45-4;  -5  53   19-2 
—  5  14  21.2      63  14  54-1  ;  -5  52  37.4 

-1088.7 
-     41-8 

978.3     -      -    I 

1083.8     .      .    1 

1 

27     y  Tauri,  1.     .     - 

1663, 
Mar.  14 

10  35     7 
I  10    4  48 

9  20  31 

i   '      ■      ■ 

63  4!  34. S      62  58  32.1,   -5  53  27-f 
-5  14  22.4      63  14  33-0'  -5   !7     0-5 

—  960.9 

-  387-1 

978.2     .      .    , 
1031.3 i   .      ,    1 

28     f'  A(iuarii,  I. 

1663, 

.Aug.  18 

9  15  37 
19    4     4 

1 
.811 

!  .    ,    . 

325  32  21.2    325  3')    9-8     -0  26  21.9 
+0  25     5.0'  325  47  37-1  !   -0  15  47-5 

-  687.3 

-  634.4 

924.2  145.6  j 

935.2  180.2 

1 

29  •    f'  Aquaril,  E. 

1663, 
Aug.:8 

10     5  31 
19  54    6 

8  50  55 

325  59     "-5     325   57     8.2     -0  27  59. C 
+  02525.9     325  47  37-1  '   -0  '5  47-; 

'+  571-I 

;-  732-1 

1  925.6;   .      .   I 

i  928.8  1    .       .  .! 

30     1  Tauri,  1. 

1664, 
Mar.  31 

9  24  20 
Uo     3  51 

',8    9  44 

1 

65  31   39-9',     f'4  49  3f'-S;   -5  34  27-5  -  9f''J-4 
-45542-3       f'5     5  43-2     -5  29  29.7'-  297.8 

1  969.8  '  11.6  ! 

1007.2:    53.5    ; 

31      (I  Tauri,  E.     . 

1664, 
Mar.  31 

!  10  16    t 
.  10  55  4! 

:  9     1  3U 

1 

b(>     2     S.9       652018.0     -5  35   55-2,+  874.8 
-45458.5'     f'5     5  43-2     -52929.7-385-5 

.967.8^    .        .    1 

1    952.3      -        - 

1 

,  32     Not  identified 

1671, 
Mar.  I. 

19     3  3-1 
\      8  33  I 

ii  7  43  5f 

; 

)  •   - 

4ft  30  41.8      45  43  50.9     +3     2  55.8          .      . 
+  3  35  38.8 '         - 

989.0  J354.O  I 

.        .   1    52.3 

1 

33     Not  identified 

1671, 
1  Mar.  I 

1963 
>.'    8  36  I 

?^  7  52 

4f'  32  33-2       45  45  38-2     +3     2  57-3 
+  3  35  4f>-3 • 

988,91    .        . 

'        '          "        "    i 

34     Not  identified 

!   1671, 
'  Mar.  I 

!    9  55  2 
4      9  25  I 

5     8  40  4 

5     •     - 

3      47     2  12.4;     40  15     0-5     +3     2  29. 
+  3  37  46.4         .      •        "I       •      ■        • 

4 

j 

986.5       . 

1 

2o8 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 
Tabular  Exhibit  of  Reduction  of  the  Occultations — Continued, 


L_ 

HEVELIUS  AT  DANTZIG-Continued. 

i 
1 

1 

INo. 

1 

1 
1 

Siar  DCciiltrtl, 

nalo. 

i 

Local  Mean  and 
1  Sidereal  Times. 

Greenwich  Me? 
Time. 

Moon's  Tabular 

Geocentric 

Position. 

Apparent    Position  of     ' 

Moon  and  Slar.               /*  — /, 

,   *-* 

I.o[rgitU(k-s.  1     Latitudes, 

5- 

i  35 

(I  ViiHinis,  I. 

1671, 

h    in     s 
10  47     I 

i 
h  m    s 
9  32  25 

198  4n  21.9 

199     0  50.5     -2     5     5.2  -   897,6 

88g,4 

— —  - 

32.4 

i 

.•\pr.  22 

12  50  45     .      .      , 

—  I    21    22.1 

199  15  48,1     -2     I  4f'.4  —   198,8    918.7 

166,9 

30 

n  Virgitiis,  !■]. 

1 67 1 , 

!  11   5&  30 

10  41   54 

199    14   31.7 

199  26   19,6     -2   II  39.2   4-   631.5'  889,1 

' 

1 

Apr.  22 

14     0  26     .      .      . 

—  I    24   22.7 

199   15  48.1  1   -2     I   46.4   -    592.8  1  865,8 

•    • 

37 

I'l.Ccl.,  16,4',  I 

lf>72, 

12  36  33   II   21    57 

54  47   10.4 

54  37     f'.jj   +4  28  33.6  _   ,,2;.  7 

l(X)4.S 

223.9 

Nov.    ;; 

3  4"   15      .      .      • 

t  4   57  574 

54  52  32.2,    4-4   19  54.1  ;+   5iq.5 

1059.5 

191-5 

i38 

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1672, 

12    4S    18    II    33    42 

54  54  37.2 

54  42  42.<>,   +.1  29     2. oi— 1056.6 

1004.7 

, 

Nov,  5 

3  52    s  i  .     •     . 

+  4  58     3.0 

55     0  i3.6     4-4  29    4.6  -       2,6 '1053,4 

39 

PI,  Mala,  20,-,  I. 

1672, 

13     7     4  II   52  28 

55     (J  If).  2 

1                                           1 
54   51   39.7i   +4  29  45.2   -   935.1    1004.6 

. 

Nov,  5 

4  10  51      . 

+  4  58  11.9 

55     7   14.8     -t-4  21   23.3!-)-    501.9  [05S.3 

•    . 

40 

PI.  Tay.,  I.J,-.  1. 

X'73, 

S     5    H. 

f)  51    I" 

55  3"  31.7 

54  49  24.9     -f  4  41   21.0  —  640.8 

9f'3.3       2.5 

! 

Mai.  22 

S     S  51 

,      .     . 

+  5   10  52.8 

55     0     5.7     +4  29     6,0;.)-    735.0 

974.5     52.5 

41 

PI.  Tay.,  IS  w,  I. 

"f'TJ. 

S     8  4f) 

•■  54  I" 

55  32  15.8 

54  50  58.8     +4  41    13,4  —   8()S.5 

963.2;   .      . 

Mar.  22 

S   II   53 

.     .      . 

+  5   10  53.0 

55     4  27.3     +4  51     0.2  -   586.8 

1 

99f'.5      •      ■ 

42 

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S   19  4C) 

7     5   10 

55  38  36.3 

54  56  44.8     +4  40  45. oj-  S31.2 

962. 8 

.Mar.  22 

S  22  54 

+  5   I"  53.4 

55    10  36.0     44  32     5,1    +    519. y 

978.2     .      . 

■••' 

PI.  .Asl.,  22  /,  I. 

■  '■73. 

S  .24  4f) 

7  10  10 

55  41   29.1 

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I 

Mar.  22 

8  27  55 

+  5    10  53. fi 

55    12     7.2     +4  30     6.oj-t-   625,1     9S5.8'   .      . 

44 

PI.  Kk-c,  17/.,  I. 

1674, 

13.41   29 

12  26  53 

54    20   22.  f) 

54  37   12. S     +4     3  26.01-   907.3     923.4  150.6 

Aug.  23 

23  51  42 

+  4  42  5f'-3 

54   52  20.1      -1-4     9  24.4   -   35S.4'  973.4  264.3 

45  1 

Pl.Ccl..  10^,1. 

lf'74. 

14     8  59 

12  54  23 

54  34  48. 2 

54  49  36.5     +4     4  38.5   -    247.4 

9244     .      . 

1 
! 

Aug,  23 

0  19  I& 

+  4  42  23.0 

54   53  43.9     +4   I'J  55.9  -  917.4 

949.5     .      . 

46  , 

PI,  M.-i.,23./,  I. 

■f'74, 

14   25  59 

13   II   23 

54  43  43.'i 

54   56  5f'.3     +4     5  22.6  |-   758.3 

925-0 j   .     .   i 

AiiK.23 

0  36  19 

+  4  42     2.5 

55     9  34-6     +3  55  22.1 

4-   600.5 

965.8'   .      .   1 

,                          1 

47 

PI.  Cel.,  ifi^',  E. 

if'74, 

14  32  29 

13   17  53 

54  47     9.2 

54  59  5f'.7     +4     5  42.6 

+   372.8 

925.1 :  •■  .  j 

1 
1 

Aug.  23 

0  42  50 

+  4  41    58. 2 

54  53  43-9     +4   19  55.9   -   853.3     929.0 

j 

4S  ' 

PI,  Maia,  2o,',  I. 

1674. 

14  43  59 

13  29  23 

54   53   10.9 

55     4  53.7     +4     f'  10.91-   212.8 

925 . 5 ; 

Aug.  23 

0  54  22 

.      .      . 

+  4  41  44-0 

5;     S  26.5     4-4  21   25.3,-   914.4 

938.4 

1 

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If'74, 

14  51  29 

13  3f'  53, 

54  57     72 

55     S     6.3     4-4     6  29.2'  1     946.2 

925.7! 

1 

1 

Aug.  23 

I      I   53 

•      •      ■  , 

+  4   41   34.7 

54  52  20.1     4-4     9  24.4  .        175,2 

959-8 

.    . 

50 

Pl,.\Icy.,25;;,T, 

■''74, 

15     I  29 

13  4(i  53 

55      2   22. f) 

55   12  21.3     4-4     6  52.9 :       888. 3 

926.0 j 

*      '    1 

Aug.  23 

I    II   55 

! 

+  4  41   221 

55  27     9.6     4-4      I     4.1    +    348.5 

952.2 1 

•   •  1 

51 

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If'74, 

'5     4  29 

13  49  53 

55     3  5f'.5 

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926.1  \ 

150.6 

i 

A  ug.  23 

I    14  56 

+  4  41    18. f) 

55     8  26.4     4-4  21   25.3!-   865.0' 

918.4' 

264.5 

52 

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14     2   13 

55    10  25.3 

55    18  47.0     4-4     7  28.2   4-    552.5 

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. 

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+  4  41     3.3 

55     9  34.5     +3  55  22.1    4-    726.1 

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55      85  (iciniiioiuiii,  I.        I'i75. 
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57  85  Cfiuinuiiini,  K.      i'i7-' 

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1683,       9  56     ?       8  41   32         65   19  27. i]     65     4  42.4    -5  28  57.0-1031.81  968.3389.9 


Jan.  9 

1683, 
Jan.  9 


5   i( 


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II     9  23       9  54  47         '''1     '  43-3|     fiS  37   '7.1:   -5  37     0.8 
.      .      .        -4  53     6.6     65  31   54. 3I   -5  39  33.0 


6  27 


1683,    I  9  58  20 
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8  ,3  44 


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1&83, 
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1083, 
Apr.  2 


10  31  5'' 


2u  30  79  36  49. 


I!     7'''  5')  55-91 


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1 

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66.0 


133 


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-4     2  42.(1,     79  16  52.1     -4  47  46.1    t-   2I9.3'I036.7    66.3 

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TIIK  CASSINIS  .\.\l)  OTllKUS  .\T  TllK  I'AKIS  OMSKKVATORY. 


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I 

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81 


I.conis,  IC. 


82  S.iiiirn,  1. 

83  Saliirn,  E. 

S4      I.alandu  1214S 


85 


86 


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,"  (".cininoniin,  I. 


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1675,   8  18  iS   8  S  57 


I(i7(>,   10  32  iS   10  22  5 

Frii.  29  9  10  19.4  . 

1676,  II  29  24   II  20 

Fel).  29  10  7  34.8  . 

1678,   7  30  21   .   . 
Feb.  27  6  2  1.3  . 

1678,   8  42  21   .   . 

Fel).  27  7  14  13.1'  , 


1680,  10  27  43  Uo  18  2 

Apr.  4  II  23  50. 4I  .  . 

1683,  12  13  50.6  12  42 

Feb.  5  9  18  43' 5  • 

16S4,  9  34  17.8    9  24  56.81     90  28  46.1 

Ouc.  21  3  39  24.7:   .      .      .     I   -o  39     6.3 


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169  3   17.2  169  39  32.0 

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.  13')- 7 

QO 

\V.  II,  if.5''    .      • 

lfi.8'),    ,  IJ  38  37 
May  31  113  39  II. 'J 

1,   2.)    l(. 
■ 

i(«.  r7    3.6 
1-5     7  3"" 

W  42      8.1: 

—  4    2(1  42.3 

.      .    i)S(i 

2     'a.  1 

.     3'^ 

')' 

iifi  Taiiri,  K. 

Ifiqo,      11    38   Ifi 

II   23  55 

85      7  2.1.7 

84  23  5().( 

+  4  27  3').; 

.      .    ()8(i 

3    24.4 

Apr,  13   13     8  2|.2 

+  5   12  5'i-4 

.84   II   23.8 

+  4     8  32. (> 

•     51)  ■8 

1)1 

87  'riiiiii,  1.  . 

Kiijo,     15     8  2() 

14  5'J     3 

55    17  4*." 

55  4f'  38 '5 

+  3  4f'  34''* 

-   (j2(.i.7    ij)l 

(1  KlI  .3 

Inly  2    21   54  3'i.'l   •      •     • 

+  4   34  51.2 

50     I    53.3 

+  3  53     7.1 

-   3')2.3  l'>"7 

(13I4.7 

1 

• 

j 
I  95 

!  96 

I 

I  ^' 

i 
i  98 

99 


93!  «i  Taiirl.I.     .      .        I&83,       7  13  52.2'  7     4  3I.2| 
Feb.  15     4  ;8  1S.5    .      .      .     i 

O'Taiiri,  I.      .      .        1O82,       7   1(1  172    7     ^'  5f'-2 
l-'cli.  15     5     (1  43.(j    .      .      . 

/i  (Jcmindinni,  I,       1(184,       ()  34   ")-2    ')  24  58,2 
Dec,  21     3  3()  26,1     .      .      , 

//  (iLMiiinonim,  IC.       1684,     10     7  58. 3    ()  58  37-3 
Dec.  21     4   13  II'.  8    .      .      . 

II  Gemiiiorum,  1.      i'i85,       'J  3*  4')"   ')  2'j  28 
Oct.  17  23  2fi  43.3    ... 

nTaiiri,  I.      .      .        ifxw,  13  44  4i'-8  13  35   'O-^ 

.\iig.  18  23  35     IJ-''    ■      •      ■ 

aTauri,  E.     .             idyi),  14  22  .|(i.S  14   13  ii).S 

'  Alls  18 

(1  Tauri,!.      .      .        I7i'i.     17  59  25.3  17  5o    4-3 
Sept.  22    6    fi  41'- 8    - 

n  Tauri,  E-     .      .        17^1-     1845438183(122.8 
Sept.  22    h  53    (i.ij    .      - 

Jupiter,!-       .      .       1715,  13  38  38-3 '3  2.j  17-3 

Jill)'  24 

Iupiter,E.      .      .        1715,  14  15     3-814     5  42-8 

J"ly24 

B- A.  C.  8184,  I.    I    1718,      84244-'    83323.1 
I  Sept.  9  19  :(i  45^    ■     • 


103 


104 


I.A   HIRE. 

(>3  27  54. ('1 
-5   17  4"-i| 

(13   13  44-5 
63  30  34.7 

-5  48     7-9-l'^l'->-2 
-5  4(>  53-"-      74.7 

973-3327  7 
1008.2    95.8 

63  29  18.8 
-5   17  40.(1 

63  14  45-8 
(■>3  3"  55. f 

-5  48     4-8-   970-0 
-5  52  31.8  +   2(17.(1 

973-3    -      • 
1001. 3|   . 

i 
()(i  28  4fi.5 

—  0  39     6.21 

90  JO  17. 8, 
(JO  54  17.9 

-1     5  55-1  -    2|0.1 
-0  51     2.4  —   8(j2.7 

911. 4 
924.2 

271 .11 
17')') 

9"  45  58.5 
-11  37  31.5 

91     3     7.4 
9"  54   17  9 

-I     315-3+    529-5' 
—  (1  51     2.4  —    73211 

912.1 
(J04 . 2 

85  44     7-8 
+  0  26  5(1- 1 

86  18  38. 8 
8fi  33  49-3 

—I)    12   22.5  —    910.5 
—  0   12    1(1.2  —        (1.3 

889. 1  205.2 
910  5  241 .3 

(14  56  17-2 

-4  57  48-5 

(15  25   52.2 
fi5  35  3<>-3 

-5   42  42.0-    578.1 
-5  29  17.2  ■-   804. 8 

(J72.5  146.1 
(J89.5279.5 

(■15    i3  35-8 
.   -4   58  2(1.7 

65  4(1     3-1 
(■15  35  31)- 3 

-5  41    1S.4   t-   (132. f 
-5  29  17.2  -   721.2 

974-3    .      ■ 
957-4    -      - 

fi5  49  34-8 
-4  49  4(1.9 

f)5  27  50.1 
(15  37  27.4 

-5   "7  15-4  -    577-3 
—  5  29   1(1.8  +    721.4 

914-3  i7')-5 
922.  5  i*.i6. 1 

6(1   13  21 .0 
-4  49     2.1 

(15  45  3'>-(i 
(15  37  27.4 

-5   !('  33-5  +   483.2 
-5  29  1(1.8  ^    763.3 

9l3-(     -      ■ 

902 . 2     . 

,      51    34  38.5 

—  0   22    54.8 

52     I   38.4 

-I    12   28.8            .       . 

973.0  121.  1 
.        .  2(JO 

5      51    55  54-5 

(J74.;  .    ■ 

-0  24  47-4 



347     <>  21-4 
—  0     5   15-' 

347     8  35.4 

'  347   '7  20.5 

1 

-0  55     5-1  -    525-' 
-I     7     6.3   h   721.: 

888.  7  166.6 

891 .()  1S0.7 

i 

:  1  2 

* 
RESKARCHES  ON  THE  MOTION  OF  THE  MOON, 

Tahilar  Ex/il/rt  of  Rediutioii  of  f/ir  Ortii//atlons  —  Co\\{m\M:A. 

CASSINI,  ETC.-SERIESII                                                                           .      | 

N(i.  j      Star  occulieil. 

Local  Mean  and 
Sider'.'al  Times. 

(Ireenwich  Mean 
Time, 

.2 

S   -     ■           .Apparent    Position  of 

j2   S  .=                 .Moon  and  Star. 

1              1 

/■-/.       :         .V               0 
/,_/,■               /)           /,_0 

^                  Longitudes      Latitudes. 

!            i            ^ 

1 

I 

//    ni     .'         //     HI     s            ° 

„ 

ro5 

33  ('a|)ii<:orni,  1, 

1705,      15  23  5S      IS   14  57        313  'S  20.7    312  34  t?i).fi    -5  30     7.4 

—696.2   99S.2    . 

Aug.  4i  0  17  44-     ■      •      •      :   -4  4S  3I--I    312  a''     5-?    -  S    '7  37-' 

— 719.S  1021 . 1    . 

lijf)  i  r  A(|uarii,  I. 

1705,    ill  4S  5'i      1'   31)  35        334  3'''  37-7    334   >5  32. &    -5  4<)  '7-5 

-837.31012.1     . 

i 

Sept.  2  22  36  27        ...         —4  5S  2..?    334  2Q  30.1     —5  3()     2.1, 

—  614.6  1035.3,  . 

1 
107     r  .\(|uarii,  I". 

170;,       12    50    II)        12    40    5S          335    15    ,10. 1)     334    45    11. 0     -S    44    2S.C 

+  940.9  loi  1.6    . 

1 

Sept.  2  23  3S     0.3    ...         -4  57  5f'.-     ■'34  2q  30.1     -5  3q     2.1) 

-325.6    991.3    . 

liiS     (,'  -laiiri,  I,      .      . 

I7i;fi,      II    13  34      II     4    13     '     64  28   ili.o      (,3  53  56. c     +0  45  20.2 

-713.9    956. 8    . 

Jai,    23     7  24  46.  c     .      .      .      ,   +1    10  23.8      64     5  50.4     +0  35    44.8 

+  575.4    916,.'.    , 

11)1)     '  f'ani-ci,  I,     .      . 

i7of.,      12  31    ;t      12  22  33        117  34   14.5    117  21)  5(,.4     +4   12   Ii.c) 

-784.7    927.4     . 

Jan.  27     8  51)     5.0    .      .      .        +4  3ft  33.1    117  43     4.1     +4  21     7.4 

-535.5    94S.2    . 

1  III  '    //  I.fclllis,  I.      . 

I7of),       g     I     1)        5  51   48        143  3fi     0.5    143  35  20. S    +4  42   10.8 

-771.7    9'".<' 

Apr.2i  lio  58  56.7,    .      .      .      ■    +5    12  27. f     143  48  21    5     +4  50  Sf'.'J 

-526.1    931. S    . 

The  ahove  limes  1 

ave  been  computed  usinj;  C.vssiNi's  coruction  for  deviation  of  quadrant      if,  instead  of  this 

, 

we  use  llie  deviation  found  on  and  after  May,  1706,  the  results  will  lie  as  follows: — 

1 1 1      33  C'apricorni,  I. 

1705,      15   24  20      15   14  59        313   18  34.5    312  34  41.8 

-5  30     6.6     ■  •  .  ,,c    998.! 

32.1 

AuR.  4     0   18     0.2    ,      .      ,      ,   -4  48  34-7    3'2  4f)     5.S 

-5    17  37  <     -740r  1012.3 

30.7 

112 

'  A<iiiarii,  I. 

1705,      II   41)   11      n  3g  50       334  3f>  47o    334   I5  3i.' 

-  5    49    17.0     —830.  :    IOI2.C 

f  0.0 

Sept.    2    22    3f)   42.0     .        .        .       1    -4    58    22.7     334    2()   30. -1      -5    3()      2.1)     -IJI4.I    I02l).5 

■'4.5 

"3 

"  Ai|iiarii,  E. 

1705,      12  50  34      12  4t    13     i  335   15   51)4    334  45   i8.^^    -5  41  27.3 

+  948.2  101 1  .6 

Sept.  2  23  38   15.3    .      .      .      1  —4  57  56.0    334  21)  30.1 

-5   30     2.9 

-324.4    997.5 

IM 

*'  Tanri,  I.      .      . 

1706,      II    13   52      II.  4   31      I     042826.1      f)3  54     4.6 

+0  45   19.2 

-705.?    95'>.f 

03.4 

Jan.  23     7  25     4.6    .      .      .         +1    10  24.f1      64     5   50.4 

+  0  35  44.8    +574.4    ()0<).' 

20.7 

'I5 

h'  Tanri,  I.     . 

1706,      II    36   15      11   2f)  54     1     64   40  59  3      ()4     4   17. c) 

+  c  45  46.6 

-   72. f    956. c 

1 

Jan.  23  :  7  47  31.3    .      .      .         +1    II   29.3      fi4     5  30.7 

1 

+0  30     6. 1 

+  940.5    943-3 

ilf) 

k-  Tanri,  I.     . 

1706,      113658      II  27  37          644123.5      64     4  37') 
Jan,  23     7  48  14.4;   .      ,      ,        +1   u  31,4      64     5  30.7 

+  0  45  47.4 
+  0  30     6.1 

-   52.8    955.? 
+941. 3!  942. f 

( 

; ;                                                    117 

«-'  Tanri,  E.    . 

'                    1 
1706,      tl    46     8      II  36  47     j     64  46   52.0      64     S  53.5 

Jan.  23     7  C7  25.9    .      .      .        +1    II   57.9     64     5  30.7 

+  "  ^5   55-9 
+  0  30     6. 1 

+  202.  f    055 -t 
+  949. f    97'. 2 

• 

118 

/  Cancri,  I.     . 

1706,     .12   32    12      112   22   51          117   34   24.  Ij    I  17  30     6.4 

+  4   12     9.3 

-777.7    927  4 

07.5 

Jan.  27     8  59  23.8 

•     •      • 

-^4  3f>  33.4!   117     3     4.1 

+  4  2"     7.4 

-538.1    943.8 

70.2 

no 

n  Lconis,  I.   . 

1706,      9     I  29 

8  52     8 

143  36  10.5'   143  35  37.7 

+  4  4^     8.8 

-;63.8|  uio.c 

31.2 

Apr.2i 

10  59  16,6 

, 

+  5    12    27.7     143    48    21.? 

+  4  .=  1)  55.5 

-526.7    925.7 

12.6 

120 

;/  Lconis,  E.   .     . 

1706, 

9  55     5     1  9  45  44 

144     3  23  3    143  5O     7..S 

+  4  38     5.7 

+  466.3    908. c 

.      .   { 

Apr,2i  jri  53     1,6 

1 

+  5    12      3.8     143  48   21.5 

-r4   50  55.! 

-769.8:  899.2 

t 
•   1 

12t 

?.  Vir^inis,  I. 

1706,    jio  47  51 

10  38  30 

212  34  3i)-4    212  43     0.9 

+  0  18  36.5 

-   518.5!  S94.7 

63.1 

May  24 

14  56    a. 5 

+  1      5  40, 3j    212   51    39.4 

+  0  30  1:4.7 

-   738.2 

902 . 2 

■49.8 

kF.SKARClinS  ON  TIIK  MOTION  OF  THE  MOON. 
labular  Exiiibit  of  Rcduition  of  tin-  Occullatums — CloiUinued. 


21' 


•ASSINI,  ETC.— SERIES  II— ("ontiniiecl. 


No.        Sl;ir  orculteii. 


133 


'34 


1  i 

a 
H 

C 
I 


~    H 


122  "  Pisciuni,  1. 

123  />  Aiiclis.  I.     . 

124  "  Scorpii,  1.    . 

125  "  Scorjjii,  E.  . 

126  Venus.  Ii. 

127  Venus,  I.. 

12S  ATauri.E.     .      . 

12(;    "  Leonis,  I.    . 

t 
130    "  A<|uaiii,  T. 

131  PI.  M;.ia,  20.-,I. 

132  ri.  Tay.,  1,1  c.  I. 


22  !,  I. 


22  /   E. 


13;     I'l.  Mnia,  20  ,.  E. 


136    PI.  Elcc,  11  Ik  I. 


137 


22  /,  1. 


138     PI.  Asl.,  21  k,  I. 


139    PI    Ast  ,  21  /•,  E 


.Apparent    Posilion  of 
.Moon  anil  Siai. 


Longiliuli's.      Latiludus. 


/>  -  H 


h    in    5      li     1)1     s 
i7ofi,      1 1    57  2t)      11  4S     5 

Nov.  17     3  43  3')- 2    .      .      . 

1707,       8  21    13        8   II    52 

Apr.   4     'J  I"  55.4    •      •      • 

1707,       7  4f'  54        7  37   33 
Sept.  3   'S  35  47-2    •      •      • 

1707,  8  35     6        8  2;  45 
Sept.  3    "3  -4     "•"     .      •      ' 

1706,      7  17  38       :    S  17 
Fell.  23     5  28  30.4    .      .      . 

1708,  7   17  53        7     S  32 
Feb. 23     5  2S  45        ... 

1708,  y  3f'  >fi       9  2f>  55 
Sept.  6  20  40  if)        ... 

I7oq,       7   5"  27        7  4i      <' 
Apr.20     9  45    10.2    .      .      . 

1709,  12     I   48      II   52  27 
Sept.  If)  23  44  4»2    .      .      . 

1709,       S   IS  32        8911 
Sept.  23  20  28  23.4    . 

1709,       8  22  34        8   "3   '3 
Sept.  23  20  32  24         ... 

1709,       8  41   24        S   32     3 
Sept.  23  20  51    19. 1     .      .      . 

1709,       9     5   32        8  56   II 
Sept. 23  21    15  3I-'     •      •      ■ 

1709,  9     8     5        8   5?  4) 
Sept. 23  21    IS     4.5    .      .      . 

1710,  4  42   1')       4  32   5S 
Dec.    J   21   34  29.f>    .      .      . 

171".       5   40  3>        5  3'    i<) 
Dee.    4    22  32  5 I.I     . 

1710,       5  49     S        5  39  47 
Dec.    4  22  41  49.5    .      .      . 

1710,       ()     2     o        5  52  39 
Dee.   4  22  54  23.7    .      .      . 


n 


0 
/.-© 


1008.5I235.0 


1025 .7  148.6 

996.01   14.3 
1005.9    28.5 

889.6'lf)0.5 
905.3'  85. 2 


23  58  34.0      23  22  46. S    -I    32   54.4-   9'''9-5 
-I      3   12. P      23  38  56.3    -I    38   30.3+    335.9 

43  25   52-S      42  34   '4.9    +'      2  43.7  -   S96.3 
+  1   33  3f'-i      42  49  ■'•2    +1    10  20.(1-   45f>-9 

245  43   l'>-4    245  31   27.7    -4  43  36  3-    5f>9.9 

-1  51    23.8    245  40  57-6    -4  31    51-5-    7"4.8 

I 

246  7     3-8    245  49  24-1     -4  43   54-2+    SOfi-SJ  888. 4j    .      I 

-3  52   50.3    245  40  57. fi    —4  31    51.5-   722.7!  881.0,   .      . 

359  32  39.2    358  41  23.2    -I    II     2.1  -   842.8;  933-3|334-2 
-o  46  37.1    358  55  26.0    -I      3  5'>-l  -   432.0    947-1     24.7 

359  32  47."    358  41   3<)-9    -1    "      '•f'-   835.9;  933-3 
-o  46  37. S    358  55  26.8    -I      3  50.0-   431-61  940-7 

635322.1      64  19  54-1    +3  55     9-8+io'5-oi  958-IJ164-2  ; 
+  4  46  48.6      64     2  59.1     +3  59  16-4  -    246.6^!042.2'259.9  i 

i()6  46   11.3    167    15   49-3    -o  21   21.3-   69f'-9|  985. Sj  30.5  | 
-,  ,)  II      9.0    if-7  27  26.2    -o  33  22.5  +    721.2^1003.0:137.0  ' 

331  39  29.6   331    10    8.5    —I   27   16.0-   622  4,  88g.S|i73.7  j 
-o  48  34.8   331  20  30.9    -I   12  49-2  -   S66.8|lo67.0ji57.6  \ 

54  59  50.1      55  24  II. 3    +4   14     8.6-   816.6    921.1180.5  | 
+  5     4     3-9      55  37  47-9    +4  21    35-f'-   447-0|  928.91235.1  \ 

55  I    59.0      55  26  33.6    +4   14  24.1  -   2f)S.2J  921.3J180.5  ! 

+  5     4     7-"      55  3>      '-8    +4  29  16.7-   892. 6|  93I.9i235-0 

j  I 

55   12     I.o      55  37  311-8    +4   15   37-5-   332 -Sj  922.1    .      .    1 

+  5     4  21.4  55  43  3*'  +4  30  16-''-  879-3!  939-9    ■      •   ; 

55  24  53.7  55  51  14-0  +4   "7   18.4+  49"-4    923-2|    -      . 

+  5     4  39-5  55  43  3-f'  +4  3"  16. 8-  778-4    9>9-2i   •      • 

55  26  14.!^  55   52  38.9  +4   17  29.4  +  891-0,  923-31   ■      • 

+  5     4  41.4  55  37  47-9  '4  21   35-f'-  246-2    922.0;    .      . 

54  \2  23.6  55     8  13. 1  -^4   13   13-7-  836.4    899.9252.2 
+  4  58  13-c  55  22  59.5  +4     9  36.8+  216.9)  910.31163.2 

55  12     1-7      55   37  30-5    +4   16  35-4-   401-3'  90*-4 
+  4   57  46-0      55  44   il-8    +4   3"  18.9-   >23-5!  915-4 

55   16  25.3      55  41   40.0    +4    17     7-'  -     60.6    902.7 
+  4   57  41.0      55  42  40.6    +4  32   18.0-   910.9    9'2-9l 

55  22   58. 4      55  47  46.8    +4   '7   55-5+    3"6.2    903-1 
+  4  57   35.7      55  42  40-6    +4  32   18.0-   862.5    915.2 


214 


RKSEARCIIES  OS  THE  MOTION  OF  THE  MOON. 
7ir,'.,/(ir  Kxhihit  of  Raitictioii  of  the  Occiiltations — C'oiitiiiued. 


'53    Jiip'"-"''.  '• 

i 

154  :  Jupiter,  I. 

I 

155  Jupiter,  E.      . 

156  I  Jiipiler,  E.     . 
i 

157  (1  Ai|ii;>rii,  1. 

i         i 


>7>5.  '5 

July  21  23 

'715.  '3 

July  24  21 

1715.  "3 

July  24  21 

1715.  14 

July  24  22 

I7i5,  14 

July  24  22 

'7'5.  " 

Auk.  15  2' 


5"   5' 

48  50. 

37  59. 
ifi  2U. 

V)  '5. 
■17  42- 

23  4f). 

32  2o. 

25      2. 

33  37. 

55  55 
30  49. 


15   42   31  > 
I      .       .       . 

S13    2S    3S.S 
()     .        .        . 

S  r3  21)  54.8 

S    .      .      . 

5  14   14  25-5 
S    .      .      . 

5  14   '5  41-5 


1 1   46  34 


10  30 

13-4 

19 

21  33-3 

+  2 

22 

26.4 

-t- 

659-3 

9S1.3 

+  3     2 

(J.I 

10 

10  34.0 

+  2 

10 

13.3 

+ 

733.1 

985.? 

5"   34 

lf).(i 

52 

I     J2.  1 

-I 

12 

23.7 

,      , 

973" 

—  0  22 

52. !■ 

•      • 

51  35 

0.() 

52 

I    Jfl.l 

—  I 

12 

28.7 

, 

973- > 

—  0  22 

56.8 

• 

•      • 

52      I 

\.U 

52 

27     fi.5 

-1 

12 

14.0 

974-9 

— 0  25 

'4-5 

•      • 

■2       I 

46.0 

52 

27  49.0 

-I 

12 

13-2 

.      . 

975.0 

-0  25 

IS. 4 

" 

• 

•      • 

.     .1 

335  28 

18.4 

335 

IS  56.2 

+  3 

53 

44. s 

- 

532.9 

980.4  142.2 

H-4  41 

49.5 

335 

27  49.I 

+4 

7 

37./ 

832.9 

9S3.oi( 

(3.3 

RliSKARCllKS  UN    TIIK  MOTION   Ol"  THK  MOON. 
Tabular  Exiiihil  oj  Kaliht'wn  of  tin-  av////(///(W/j— Coiiliiuictl. 

CASSINI,  ETC.— SERIKS  II— ronliniicil. 


215 


No.        Sl;ir  occiillcd.  Dale. 


c  ■= 


■g  i 


J*"  o 


.A|ip;ircnl   I'osiiiiin  u'f 
M<jon  ami  Slar. 


Longitudes.     Latitudes. 


/■-/. 


15S  K  Aquarii,  E. 

151J  (.•  .^i|iKirii,  I. 

l(.o  ^  Ai|uaiii,  1. 

ifii  "  Tauii,  I. 

162  n  Taiiii,  E. 


I 


/<    m      s       h  "I    s 

1715,       12    41       2        12  31    41 

Auk-  15  22   '('     3-''    ■  •      • 

1715,        S     5     cj        7  55  4S 

Oct.    <)    21    16   15. CJ    .  .      . 

1715.       7  26  56        7  17  35 

Dec.  30     2     I   14.1    .  .      . 

1717,       y     2  5S        S  53  37 

Sept.  25  21  21     4-&    •  •      • 

1717.       9  55    iS        ()    15   57 

Sept.  25  22  13  33.2    .  .      . 


163     B.  A.  C.  8184,  I.        1718,       84238       3  33 
Sept.  I)   19  5f'  39-'     •      • 


164  a  Tauri,  I. 

i 

165  u  Taur],  E.    . 

if)6  "  Tauri,  E.     . 

167  >  Tauri,  1.     . 

j 

16S  ;   Virginis,  I. 

l6g  )   VitKinis,  E, 


171,),  7  42  58  7  33  37 

Apr.  22  ij  43  54.3  ■  •      ■ 

1719,  8  32  27  S  23     6 

Apr.  22  10  33  31.4  •  •      •■ 

1711J,       y  43     5        y  33  44 
Oct.  30     o  17  23        .      .      . 

1719,  7     4  40       <>  55    "J 
No-.  2()  23  24  58.9    .      •      • 

1720,  12    24      2        12    14    41 

Apr.  20  14  20  50.5    .      .      . 

1720,     12  49  41)      12  40  28 
Apr.  20  14  46  4" -8    .      .      . 


170  PI.  Elcc,  17  fc,  I.        1727,  '4  121      1352  0 

Seiit.  f)  I  3  42.1     .      .  . 

171  1>1.  Cel.,  lO  ,(,',  I.         1727.  '4  711      13  57  5" 
Sepi.  6  I  9  331    •      ■  • 


172  Pl.Tay.,  H)<-,  1.   .        1727.      '440     5      M  3"  44 

Sept.  6     I   42  32-5    •  ■      • 

173  PI.  Maia,  20  ,-,  I.        1727.     '4  42   ifi      14  32  55 

Sept.  (t     I   44  43.8    .  .      ■ 

174I  PI.  Elec,  17 /',  E.   1727.  >5  10  '5   '5  "54 

Sept.  (>     2  12  47-4  •  •   • 

175'  PI.  Cel'.,  l(),i,',  E.   1727.  '5  20  39   15  11  "8 

j              (  Sept.  6  a  23  13- >  •  ■   ■ 


335  55  i'>-3 
+-4  4"  59-3 

335  21  14.1 
+  4  47  33-2 

335  58  5-1 
+  4  32  20.  1 

65  5  53.6 
-4  3<>  58.0 

f>5  3:  34.9 
-4  38  17-2 

347  "  '3-3 
-o  5  15-3 

66  20  37.3 
-5  5  l-l 

66  46  21.3 
-5  4  57-''' 

65  41  17.3 
-4  55  43-' 

61  14  15.3 
-4  i<>  4.8 
1S6  to  47.0 
+  3  53  48.0 
186  26  49.2 
+  3  54  41-2 

55  7  ('•4 
+  4  44  15-7 

55  10  9.8 
+  4  44  23.2 

55  27  25.5 
+  4  45  5'7 

55  28  34.0 
+  4  45  8.3 

55  43  14.5 
+  4  45  43'9 

55  48  42.1 
+  4  45  57.' 


335  38  53-9 
335  27  49.1 


335  14  4-7 

335  27  52.5 

335  12  49. S 
335  27  3('-') 

65  34  44-8 

65  50  52. 8 

66  6  26.0 
65  50  52. S 

347  8  32.3 

347  17  20.4 

65  38  20.2 

65  51  45-8 

66  3  25.8 
6;  51  45-8 

66  6  35.0 
65  52  47-" 

61  40  20.4 
61  53  30.8 

1S6  ti  16.5 
186  16  53.8 

186  23  53.4 
186  16  53.8 

55  21  32-1 
55  3f>  47.7 

55  23  55.9 
55  38  II-5 

55  37  II-4 

55  45  57-8 

55  38  3-3 
55  52  54.') 
55  48  59.6 
55  S*)  47.7 


+  3  55  37-0 
+  4  7  37.7 

+  3  58  40.0 
+  4  7  39-" 

+  4  I  4'-7 
+  4  7  39.1 

-5  27  15.9 

—  5  29  12.6 

—  5  26  2().0 

—  5  29  12.6 

-o  55  4.9 
-1  7  0.4 

-5  3''  44-1 
-5  29  15.1 

-5  38  46.1 
-5  29  15.1 

-5  35  3-4 
—  5  29  12.9 

-5  38  14-7 
-5  45  47-7 

+  3  4  44.3 
+  2  49  1-7 

-r  3  4  4-2 
+  2  49  ' • 7 

+  4  13  4-4 
+  4  9  41.5 

+  4  13  36.2 
+  4  20  12.7 

+  4  16  28. 9 
+  4  29  23.1 

+  4  If)  39'9 
4-4  21  41.9 

+  4  iS  57-8 
+  4  9  41-5 


+  664.S 
-720.7 
-827.8 
-539.0 

-887.1 
-357-4 
-968.0 
+  116.7 

J- 933. 2 
+  166.6 

-52S.1 
+  721.; 
— S05.6 
— 449-0 
+  700.0 
—  571.0 

+  82S.0 
-350-5 
-790.4 
+  453.0 


■V  0 

/>      l.-Q 


981.0    . 
979-4    •      . 

981.2  195.8 
985.8139.7  j 

942.S278.4  ; 
954.2    57.1 

953'4  182.5 
970.6243.3  ^ 

956.9    .      .   j 
943-5     ■      • 

858.7  166.6 
894. 1  I  So. 7 

910.3    31.9 
919.0    34.0  I 

qoS . 6     . 

900.8  . 

900.0  216.7 
81)5.6  209.2  ' 

899.5243.9 

907.6  178.0 


55  53    "-7 
55  38  11-5 


+4  19  47-1 
+4  20  12.7 


-337-3 
+  942.6 

+  419-') 

+  902 . 5 

—915.6 
+  202.9 

-855.6 
-39f'-5 
-526.4 
-774-2 

-890.7' 

—  302.0 

+  73I-9 
+  55(J-3 

+  SS9.2' 

—  25.6 


1003.2    31.2 
tool. 0155. 1 

1002.7    . 
995.1    .      . 

924.9  164.0 
935.4251.6  j 
925.0    . 
941.4    .      ■   ' 
926.0    . 
935-2    .      . 


926 . 0  . 
93S.2    .      . 

926.6  164.0 
917.6251.8 

926.8    . 

857.1  .      . 


2l6 


UESIJARCllKS  O.N  TIIH  MOIIO.N   OF  TIIK  MOON. 

'J'nhiiliu-  Exliihil  of  Kcifuitioii  (if  the  Ociultatunis — C'oiuiiuiud. 

C.XS.SINI.  KTC— SKRir:S  II— CiMiiiiiiud. 


No, 


177 


17S 


179 


I  So 


182 


Star  occulled. 

Dale. 

Local  Mean  and 
Sidereal  Times. 

Greenwicli  Mean 
Time. 

Moon's  Tabulai 
Geocentric 
Position. 

.App.ircLiI    I'ositiuti   1)1 
.\Io  ill  ami  Si.ir. 

Longitudes.     Laliliides. 

I  ~l. 
Ii-li 

1 
© 

/.-© 

//  m      X 

// 

///     s 

,      ,       ., 

., 

n 

. 

I'l.    lay.,  Iij  e,  K. 

1727. 

>5  35  5<) 

15 

26  38 

55   56  44-3 

55   58  5". 8 

+  4  20  5(1.0 

+  774. 0 

927. 1 

Scpi.  0 

2  3S  35-7 

+  4  4'J   "''.5 

55  45   57.8 

-!-4  2y  23.1 

-507.1 

923.4 

PI.  Maia,  20<-,  E, 

■727, 

i()    0  38 

15 

51    17 

5O     <)   10.5 

5O     8    12.7 

+  4    22    40.  t 

-^918.7 

927.5 

Sept.  6 

3     3  >8.7 

+  4  4f)  47.5 

55   52   54.0 

+  4  21    41. g 

+  58. g 

9>7.9 

.      • 

'I  Taiiri,  I.      . 

173S, 

<)  44  42 

9 

3;  21 

(16     0  50.1^ 

65    53  .12.1 

-5  34   lS.2 

-857.2 

903.4 

282.5 

Jan.    2 

4  33  51-4 

• 

-5     5V1.' 

(•>()     7  5().3 

-5  29   IO-4 

-307.8 

907.1 

143.6 

ti  Tauri,  E.     . 

■73S, 

11      5  57 

10 

5f'  3f' 

6()  41   44. (, 

W)  22  36. CJ 

-5  32   41.3 

+  877.6 

903.2 

. 

Jan.   2 

5   55    "J.S 

-5     5    "S-S 

f)6     7  5').  3 

--5  2g   10.4 

— 2lo.g 

8gS.5 

.      . 

(I  Taiiri,  I. 

1738, 

5  33  53 

5 

24  32 

f>5  27  45. S 

f'5   54  44-? 

-;  24  2J.3 

-845.3 

88g.6 

272.1 

Dec.  23 

23  41   5S.3 

-4  43   45.5 

fib     S  49.8 

—  5  2g  og . 8 

+  287.5 

88.g.3 

154." 

n  Tauii,  E.     . 

■  738, 

f'  33  54 

6 

24  33 

65   57  27.1 

Of)  20  43.7 

—  5  20   15.1 

+  713.9 

8g1.f1 

. 

Dec.  23 

0  42     9.2 

-4  42  41-3 

fifi     8  49. 8 

-5  2g   10.0 

^  534.9 

88g.5 

.      • 

II  Tauri 

1731). 

7     0  10 

0 

50  V) 

Vl   10  4>.4 

59     2  40.0 

-5  2g  58.5 

327.0 

Fcl).  15 

4  4'   23.; 

-5      I      7-4 

•      • 

iii.g 

DELISLE  .VT  LU.XEMHOURG. 


183 


184! 


185 


186 


187 


18S 


7  Tauri,  1. 

B.  A.  C.   1373.  I. 

')  Tauri,  1. 

i  Sagiltarii,  I. 

f  Sagiltarii,  E.     . 

I.)' Tauri,  E.     . 


189  i  '1  Cancri,  E. 


190  '  a  Tauri,  I. 


Igl  '  11  Tauri,  E.     . 


192  1  /  Geniinoriini,  1. 


1713. 
Dec.    1 

1714. 
Mar.  20 

'7'4. 
.vlar.  21 

1714. 
Apr.  fi 

17M, 
Apr.  6 

1714. 
.Sept.  27 

1714. 
Oct.   2 

1717, 


II  50 
4  4' 
g  ifi 
9     7 

10  25 

10    21 

15  2fl 
Ifl    26 

ifi  3g 
17  40 

g  10 
21   34 

14  47 
3   32 

9     3 


Sept.  25  121   21 

1717.  I  9  55 
Sept.  25  22    13 

1718,  113  33 
Jan,  15  I  g  14 


24.3  II  4g 

1.5    ,  . 

o .  2    g  f  1 

55.2  .  . 

28. g  10  ifj 

31. g    .  . 

4I.fii5  '7 

39.0    •  • 

56.316  30 

5.8    .  . 

o .  7    g  o 

56. S|   .  . 

21.3  14  38 

ss-(>:  ■  ■ 

4-3    S  53 
10. g    . 

23. o'  9  46 

38.2!   .  . 

55.0I13  24 

20.31   .  . 


3-3 


39.2 


7-9 


35.3 


39- 


0.3 


44.0 


34.7 


68 
+  0 

65 
+0 


27S 
+  2 

279 

+  2 

61 


I2g 
-4 

65 
-4 

fi5 
-4 

105 
-4 


5   59 
53  38 

■5  35. 
32   12. 

55  25. 
40  13. 

55   14 

2g  27 

36  36 
32  40 

49  47 

4  38. 

8  31. 
45     8. 

5  42. 

30  58. 

35  38. 

38   18. 

'>  55 
49  15 


,0      (.7 
8      63 

64 
f'4 


78 
78 

8    27g 
(1    27g 

.7    279 
.6    279 

.  I      62 
7      62 

3    ■2g 

6  1 2g 

7  ('5 
2       65 


.2     104 
.7     '04 


59   '('■< 
9  59-5 

33  0.2 
42   15.5 

'5  54-9 
30  ig.4 

12  36.7 
27  40.0 

42  52.2 
27  40.0 

19     5.6 

5  3.8 

52  43-4 
39  23.  I 

34  48.7 
50  52.9 

6  28.5 

50  52.9 

42  27.3 

51  12.0 


-t-  o    2g    10.8 
+  0   40    45.7 

+  "     3     ".71 

—  o    1^  54.6! 

-1  13  24.  J 

-1    ig  41.4 

+  1   35  55-7 

+  1   41  53.7 

+  1   38  3.6 

+  1   41  53.7 

-o  54  23. g 

-o  46  57. g 

-5   12  53.9 
-5     6     g.6 

—  5  27   16.2 

—  5   2g   I2.fi| 


—  5  26 

27.3 

-5  29 

12.6 

-5  25 

9.9 

-5  39 

54.0, 

-643.4  g3g. 
-6g4.g    946 

-555. 3i  g47 
+  775-3  953 
-864.5  g3i. 
+  377.0;  943- 

-903.3'  953. 
-35S.OJ  g71. 

(■gl2.2:  955. 
—  230.1,  940. 

+  841.8  g65. 
-4  4".''  952. 
+  8ix),3i  899. 
-404-31  893, 

-gf'4.2  g53. 
+  11O.4    966. 

+  935.6  956. 
+  165,3    946. 


-524.7 
+  884.7 


1014. 
102b, 


0249.4 
8178.8 

s 359.7 

6    65 

2  0.7 

5    77. 8 

4  16.5 
4  262 

3  •      • 

4  .      . 

4184.2 
5237.9 
7189.1 
631x1.6 

4182.5 
9243.3 


1  295 . 2 

o 169.6 


RESEARClll-S  ON    1  llli   MOTIDN   OF  THE  MOON. 

Tahiitar  E\lutnt  of  Kei/iiclioii  <>/  tlif  ar«/A;//,'//,(— CoiitimiL'il. 


21/ 


DF.I.ISLE  AT  LUXK.MUOURCi— Conlinued. 


No,        Sl.ir  occiilU'd. 


Dan 


l'J3 


Taiiri,  I. 


194      H.  A.  C.  8lS4,  1. 


■')5 


«  Taiiri.  I. 


Iij()  a  I'auri,  1'.. 

r()7  ;  Lilir;o.  I. 

I(j8  11  Tauri,  I. 

Kji)  'I  Tauri,  K. 

2o<)  A'  Taviii,  1. 


203 


20 ) 


20() 


207 


2o3 


209 


9  Tauri,  I. 
HI.  Klcc,  17  I',  1- 
PI.  Cfl.,  16 .v.  1. 
f'l.  Maia,  20  «,  I 
I'i.  >Kr,.23  ./,  I. 
I'l.  Alcy.,  ,,,  1.      . 
Pl.l'lcio.,  23//,  I. 
IM.  Alias,  27./,  1. 
r  Cf.niiiorum,  I. 


•3      . 
S     « 

c  .5 


Ai)|>arcnl   I'osition  of 
Moon  and  Siar. 


/■-/, 
V-B 


h   III 


Uonniludc-s.      I.aliludus. 


0 
/.-0 


A    /« 


171S,     !  f    31   35.      f>  22    15.1      f)5  35  4>-5 

Tell.    9  ,  3  4)  252    .      •      .        -4  53  48.7 

iji.S,       3  42  37.2    3  33   16.9    347     o  I3.3 


f>5  35  '"'■5  -5  25  41- 

65  51  7-9  -5  29  16. 

347     3  31.9  -o  55     5. 

)     5   I5-3i  347   17  20.6  -I      7     f>. 

I,i<),    '■  7  42  53-S;  7  33  33-5     «'  20  SS-fj     f'S  3'  '9-2  -5  3^'  44 


Sept.  9  iiy  sti  33.3: 


A|)r.22  :  9  43   ")•'); 


i.i]     65  5 r   45. S    -5  2')  15 


1719,    ;  3  32  35.4    82315.1  (i(,  4fi  25.9I     &0     331.1    -5  3''  47 

Apr.22  jio  33  3').S    ...  -5     4  57.f:     (>5   5'   4--S    -52915 

1719,    !  7  43  32.1^   7  34   ■'.*•  231      &     3.(     230  57   .4.1      t  4  20  39 

Aui,'.21  117  41   3I-''    •      ■      ■  +5    "5   I7-" 

1719.       3  4fi  49- 1    8  37  2i.S  O5   12  52  ' 

Oct.  30  1^3  20  57.!^     ...  -45')  lo-fe 


231    13     2.()    +4  24  5') 
65  40  52.6    -5  33   l<) 

65    52    46.9     -5    29    12 


94324.1    9  31     3-*'      fi5  41   27.0'     06     0  42.5    -5  35 


17"). 

Oct.  30  I  o  17  42.1:    .  . 

1725,    iI2  25,  33.2  12  16 

l-i4.   !9  jio  24  58.7,    ■  • 


-4  55  42.',. 

.9  60  8  2.9 

I  +1  44  5.5 


O5  52  46.9  —5  29  12. 

59  20  55.2  +1  9  51 
59  36  46.2  +1  13  59 


1 

-961.4 

965.9320.6 

2 

+  215.1 

93, .2  105.3 

3 

-525.7 

888. 7  166.6 

4 

4-721.1 

S94.  1  180.7 

4 

-Su6.6 

910.3    3' -9 

1 

-449-3 

920.2    3).o 

I 

+  705 .3 

903. {     .      . 

1 

—  572.0 

905.4    .      . 

s 

— H-^o 

97U.7  148.0 

7 

-259.9 

980.6    83.2 

0 

-7I4.3 

897.8  216.7 

') 

-546.1 

S96.5  209.2 

S 

4-335.6 

900.0    . 

9 

-349-9 

902.4;   .      . 

.() 

-951.0 

969.4331.5 

•4 

-247.8 

982.4;  S3. 1 

DELISI.E  AT  ST.  I'FTERSHIRG. 


.8  6  52  4S.3   53  50  3'.-*   53  22  13.0 
-+-4  12  43. 8   53  37  53.0 


1727.   "  54  ' 
Fel).27  7  2-'  12.1 

1729,   16  35  57  9|U  34  44-4   56  I  25.8  55  24  28. 3 

Dfc.  3  9  27  24.9!  ■   •  ■    +■»-»*  '-l^  55  3S  54.4 

1729,   I6  41  39.614  40  26.1   56  4  15.3  55  27  15. » 

Dec.  3  9  33  7-5  -   ■   ■    +-»  48  9-'  55  4o  17-3 

1729,      17   16  56.615   15  43.1      50  21   45.5  55  44  4S-7 

Dec.    3    10     8  30.3     ...         -t-4  47  38.9  55   54  59-9 

1729,   17  31  47--I  15  30  33-9   56  29  6.9  55  52  22.6 

Dec.  3  10  23  23. (  ...    +4  47  26.0  55  5(>  7-8 

1729,    .174313.81547     0.3      563716.5  5''     052.7 

Dec.    3   10  39  52.7    -      •     ■     '  +4  47  ii-7  5^  I3  42-8 

.     1729,      18  32  17.4  '!■>  31     3-9',     56  59     8.0  56  24  16.1 

j  Dec,    3    11   2(     3-5     -      •      -         +■»  •»'^'  32-7  50  36  55-9 

'     1729,      18  37  35-1' 'f-  3!>  22.1      57     '45-3  5&  27     8.5 

Dec.    3   11  29  22.6    .      -      -     ■   +4  40  28-"  5f'  35  31-5 

1733.    17  33     S.S    5  3"  55-3i     9258     9-i  92  48  4»-7 

Mar.22l  7  33  55.(>i   •      •     •     i  -2  3o  39-3  93    4  4f>.S 


4-3  40  29.4 
+  i  41  39-7 
+  4  13  23. 1 
4-4     9  44-1 

-1-4  13  7-0 
-t-4  20  15.2 

4-4  10  56.0 
+  4  21  44-'i 

+  4  9  58.5 
4-3  55  41.2 

-1-4  S  53.6 
-{-4      I    23 -0 

4-4  5  54.9 
4-3  5S  11.5 

44  5  33.1 
4-3  53  22.7 

-3  8  12.4 
-3     5  22.4 


-940.C 

-  70.3 

-566.1 
4-224.C 

-7S2.3 
-427. ( 

-611.2 
-64S.( 

—  225.2 
-I-S57.3 
-770,1 
-f450.c 

-759.8 
4-4f>3-4 

-503.' 
+  730-4 

■962, 1 


936.  t 
940.7 

8S8,e 

892,4 

833,6 
8S9,( 

887.1 
890 .  c 

8S7 .  ■: 
886.2 

886.8 
S90.3 

885.6 
883. J 

885.5 
886.2 

959.2 
975.7 


339.0 
74.6 

252.0 
163  6 

1O3.7 
252.0 
163.9 


252.0 
164.2 


252.0 
164.6 

2-5 
90 . 6 


75  A  I'.  'J 


2l8 

RESEARCHES  ON  THE  MOTION 

OF  THE  MOON. 

Talnilar 

Exhibit  of  Reduction  0/  the  Occitltations — C 
DKI.ISI.E  .\T  ST,  PETERSBURG— Coniiuui'i 

out 

imicd. 

. 

1 

No. 

i 
i 

St.ir  oci:uItc(-l. 

D.iti;. 

1  Local  Mean  and 
Sidereal   Times. 

Greenwich  Mean 
Time. 

1  Moon's  'I'abiilar 

'J 

■7 

.\p|).irenl    Position  of 
.Moon  and  Star. 

Longitudes      Latitudes. 

/)      /.-0 

1 
/;     HI        .V      //    III        X 

" 

1 

. 

.. 

210 

1.  Cancri,  I.    . 

173.'. 

7  27   49. f)    5  2f)  3fi.l     131 

5') 

57.7 

132 

19 

49  .S 

~5 

21  52.2 

-43''.  7 

940.6      5.4 

.Mar.  2; 

7  40  25.5     .       .      .          --4 

44 

If). 9 

132 

27 

fi.5 

-5 

35  30.1 

+  817.9 

926 . 2  1 26 

211 

11  Taiiri,  1.     . 

17,U'. 

10   |i)  54.3    S   iS  40.  S      ()6 

2S 

23. 0 

<>i 

54 

2  .  J* 

—  5 

19     5.0 

-718.0 

929.9   25.3 

Apr.  1  1 

11    52   54.3     ...          -1 

34 

4   4 

66 

6 

O.S 

—  5 

29  II .0 

+  606.0 

937-1    40.8 

212 

It  Tami,  I. 

173''. 

tS   Id   12.2  Ifi   14   5S.7      fi; 

47 

53.'" 

'■5 

^0 

41.7 

~5 

26     4.0 

-937.3 

944.3  130.0 

Au.^r.    , 

3     0   If.o    ...          -4 

4; 

7  ■  - 

6f) 

6 

22.0 

~  5 

29     7.9 

+  183.9 

951 .0  296. 1 

213* 

"  Tauri,  li.    . 

173''. 

1')  27  5". 9 '7  2I1  37-4      ''(' 

27 

12.6 

!>(> 

21 

51.0 

'"5 

25  29.5 

-1-929.0 

945.5    .      . 

.•\ug.    I 

4   12     5.=     .      .      .         -4 

4'> 

27.7 

(,(> 

6 

22.0 

~5 

29     7.9 

+  218.4 

950.2    .      . 

2I^ 

CI  Tauri.  I.     . 

>73!i. 

14  44   52.412  43  3S..,      f.(. 

1 

50.4 

(>i 

5' 

26.5 

~5 

23  59.3 

-932.5 

923.0209.9 

Oct.  22 

4   51   3^.1     ...         -4 

51 

35.1 

66 

6 

59-' 

-5 

29     3.4 

+     9.  1 

928.3  216.2 

2.5* 

n  Tauri,  E.    . 

I73f'. 

'5   59  43.413  5;^  29.9      (i(< 

41 

17.0 

66 

22 

29.9 

—  5 

29  32.4 

+  930.9 

922.7    .      . 

Oct.   22 

6     6  41.4     .,     .      .         -4 

52 

50.2 

66 

6 

59." 

—  5 

29     8.4 

—   24.0 

927.0    .      .1 

216 

a  Kconis,  I.   . 

1737. 

1)  41    ■-"■'^    -  40     7.3    137 

52 

4.(. 

137 

43 

46.  S 

-3 

14  42.9 

-927.7 

959.7    47-5 

May    7 

12  43  57.9    ...         -2 

24 

43.7 

'37 

59 

't.5 

~3 

10     0.6 

-282.3 

963.3    go. 5 

217 

Jupitei"    . 

1737. 
Mav  22 

15   50  26. S  13  55   13,3    349 
It;  5')   13.  S     .      ,      .         -0 

23 
23 

4.0 
23.4 

349 

23 

3;. 7 

-' 

16     6 . 0 

892.7    01.9 

2t3 

II'  Tauri,  I.    .      . 

1737, 

13     3  21.911      2     8.4      63  4.S 

'5.7 

f'4 

5 

45.9 

-6 

0  35. S 

-f>77.7 

903 . 0  1 20 .  2 

I»ly  22 

21     6    10.4     .      .      .          — ; 

S 

39.*' 

0( 

17 

3.6 

-5 

46  27.0 

-348.8 

1084      304.1 

219 

"'  Tauri,  !•:    .      . 

1737. 

13  35   46.1  II   34  32. f)      64 

4 

51.3 

f'4 

23 

30.4 

—  5 

59  54.7 

1-386.8 

903.9    .      . 

July  22 

21   3S  3').y    ...        -5 

3 

48.  f. 

'>4 

17 

3.'> 

~5 

46  27.0 

-807.7 

894.7    .      . 

220 

«-  Tauri.  F..  .      . 

1737. 

13  4S  22.311   47     S.H      ()4 

II 

22.(1 

fM 

30 

16.2 

—  5 

59  3fi.5 

+  7S3.S 

904.3    .      . 

July  22 

21511.3.2.      .      .         —5 

8 

52.1 

(u 

17 

'2.4 

—  5 

52     4.7 

-45'.8 

901 . 1     .      . 

221 

71  I'auri,  I.    . 

>73S. 

f)  20     4.0    4  IS  50. 5      63 

21 

44.4 

(>3  33 

34.3 

~5 

49  41.7 

-531-7 

398.6282.5 

Jan.    2 

I     S  21.3    ...         -5 

f) 

30. S 

''3 

42 

26.5 

-6 

1   45. 8 

+  724.1 

896.7141       1 

.    222 

"'  Tauri.  I.    .      . 

■  73S. 

7  29  33.5    5   23  25.0      f:3 

5f' 

39.1 

('A 

2 

3'. 6 

-5 

47     3.0 

—  909 . 2 

ipo.o    .      ,    ' 

i 
1 

Jan.    2 

2   l3     7-3    ...         -5 

f) 

23.5 

f>4 

17 

40.3 

-5 

4f)  29.8 

-33.2 

905.2  ... 

223 

((•  Tauri,  1.    .      . 

'738, 

7  32  54.5    5  31    41.0      '13 

5S 

"7.7 

64 

3 

50.7 

—  5 

4f'  55-9 

-852.2 

goo. I    .     .   j 

Jan.    2 

2  21   23. S    .      .      .         -5 

f) 

23.0 

f'4 

18 

2.9 

-5 

52     7.fi 

+  3'I.7 

9»3.3    .      - 

224 

a  A.  C.  I3yi,I. 

'73?. 

S  51     3.5    (1  49  50.0      1)4 

37 

35.2 

'>4 

34 

55.8 

-5 

44  21,0 

-801.7 

901. I    . 

i 

Jan.     2 

3  39  45. f'    .      •      .      ,    ~5 

(> 

9  7 

'U 

|3 

17.5 

—  5 

37     7.1 

-433.9 

908.2    .      .   ' 

225 

<i  Tauri,  I.     .      . 

1733. 

12  23  37.8  10  22  24.3      ()(l 

24 

30.5 

(-5 

59 

16.2 

-5 

41    30.2 

-523.0 

900.1  2S2.5 

Jan.    2 

7   12  54.9    .      .      .      1-5 

5 

25.2 

06 

7 

59-2- 

-5 

29  10.5 

-739.7 

904,5143.6 

220 

0  Tauri,  E.    . 

I7JS, 

13     3   17,8  11     2     4.3|     b'l 

44 

30.5 

66 

16 

7.8: 

-5 

41   45.7 

+  488.6 

899.4    .      - 

1 

Jan.    2 

7  52  41.4    .      .      .1-5 

5 

14.0 

66 

7 

59.2 

-5 

29   10.5 

-755.2 

898.2    .      . 

# 

iy  reffrenou  to  (lie  origiua 

notes,  it  will  be  seen  that 

the  obs 

ervei 

was  dubious 

whether 

both  emersions  were                                    | 

nol  too  late.     The  icsu 

ts  strongly  indicating  it.  Iioth  must  be  rejectc 

d. 

• 

RESEARrllKS  ON  THE  MOTION  OK  TIIK  M(K)N. 
Tabular  Exhihit  oj  Reduction  of  ///-■  Oatillatii>iis—Con\.\n\m\. 


2  19 


DELISLE  AT  ST.  I'ETERSIUJRC— Conlinmd. 


No.       Si;ir  occullcil. 


227    /lleniinoiuni,  I. 


228    71  Tauri,  I.     . 


221)    71  Tauri,  E.   . 


,230    «' Tauri,  I. 


231     "•'  Taiiii.  I. 


Date. 


.H   £ 


\l>lKiioiil    Position    of 

Moon  anil  St.ir.               /  _  / 

.V 

G 

/■■  -  /.' 

/) 

/,-0 

)ngitn<lus.      l.atitiulfs. 

1-3S 

Krl). 


232 


n  Tami,  1. 


233  «  Tauri,  I*'. 

234  "  Tauri,  1. 

'  235    (1  Tauri,  E. 

236  85(;eiuinoruni,  I. 

237  Sjdeuiinnrum,  E 
233     c'  Cancri,  1.    . 

c!  Cancri,  E.  . 
240    Pl.Elcc,  17^  I. 

I  241]  PI.  Cel„i6i',  I. 

i 

i         ' 

1242     PI.  Mer.,  23  (/,  I. 


1339 


i 


243  f- '• 

344     PI.  Alcyone,  v>  !• 


c  ■= 

r.  u< 

-  1 

►J  (/■' 


A    VI        s      h    m        s 

8     <;43.5    0     S35.0    .09  3240. S    U..J54  37.4    -4     "=5-7    -4"5.y    ■)30.23l4-<> 

5     „37.,     .      .      .         -^32410,2    no     13,1.3    -3  4f'  2S.2    --837.5    934-'>>5f'-0 

1738,      15     310.013     15''-:      ('3   '4     4-S      63  2()  33-3    -55424.?    -7'?I.2    8()3.2    .      .j 
Aug.  S     01222.3    ...         -5     .)  17.0      634234.5     -''     ■   Jf.'l    -^444.4    8,J5..     .      .| 

1733.     15  5y     5.0135752.4  f>3  4!45.l  f'3  53  44.5    -5  5143.7    +670.0894.6    •      • 

Aug.  8      1      S.27,3    .      .      .  -^     843.9  634234.5     -6     I  48.')    +605.2895.1     .      . 

,738,      .62150.7142037.=  6353     0.3  64     313.5    -55037.7    -S74.S    895.0136  2 

Aug.  S     .3115.0.      •      ■  -5     8=9.1  64   .7  48. 3    -5  4626.3    -251.4   905.9288.. 

,738,      1622     7.7.42054.2  6353     8.r  64     320,4    -55037.0    -S90.0    S95.0    .      . 

Aug.  8     .   3>   32.9    .      •      •  -5     8  29.0  64   .8   .0.4    -5   52     4.1     +   87. 1    S89.6    .      . 

.738      21   18     5.4.9.651.9  6f,  1934.9  655846.4-54050.3-559.6895.7136.2 

Aug.'s     628.9.3    ...  -5     5     7.4  66     8     6.0    -529     7.4    -702.9    896.8289.9 

173S,     22     749.320    635.8  66  44   I.. 4  66  .8  49. S    -54026.0    +643.8    894.9    •      • 

Aug. '3     7   .8   ...3    ...  -5     429.8  66     8     6.0-529     7.4    -678.6933.7    •      -I 

.73S,      .1    57  37.2    9  56  23.7  65   4.  .12.6  65   56  41.5    -5  38  .3.2    -7.0..    894.3.89.6 

0,1.    2     043     9.6    .      .      .'  -45425.3  ''<'     S3..6    -529     7.5    -545.7    892.9236.5 

1738,      .2  57  57.S.0  56  44.3  66  I.   38. 5  66  22   16.7    -5  35   II- I     +825.1    895.5     •      • 

Oct.    2      14340.0    .      .      .  -4  53  39-3  66     8  3. .6    -529     7.5    -363.6    898.2    .      .    , 

.739,      .34053.4.13939.9  .124142.4  1.3.053.3    -05855.8    -S56.5    895.32.0.2 

OC..2J     34833.1     .      -      ■  -02438.1  1.325     9.8    -05424.6    -27..2    S9S.3263.2 

4  5.    33.8.2  50  20.3    ..3  .6  26.1  113  40     6.7     -o  54  33.5    +896.9    896.8    .      .    : 

-o  21   34.3  113  25     9.?    -o  54  24.6    -     8.9    S96.8    .      . 

1739      .•...^so.c.     943.0  .24.436..  124   50  28. S    +0  2     2.3    -882.9893.52.1.2 

UCI.24  32227.8    .      .  +03632.6  .25     5   II. 7    +0  4     3.3    -126.0891.8273.9 

,7.9,      .4   .7   IS. 4  12   16     4.9  124  47  15.2  .25   .9  58.0    +0  6  33-7    +886. 3    S95.4    -      • 

Oct'^24  4  29     0.6    .      .      .  +03924.6  125     511.7    +0  4     8.3    +145.4    898.2    .      . 

,746,  82040.061926.5  56.258.4  55  37     4-7    +4  8     6,8    -S94-7    896.7      6.2 

Mar.26  83646.;     -      •      -  +4  41     2.6  55   5.59.4    +4  9  50.7    ->"3.9    898.4    49-7 

.746,  8  33     7.0    6  36  53-5  56  2.    .4.9  55  45   16.0    +4  7  48.2    -4S7.3    896.3    •      • 

Mar  26  854.5.9-      -      •  +4  -t'   24-7  555323.3+4=022.0-753.8896.9.      . 

1746,  9     751-3    7     637.8  563634.2  555933.3    +4  7     9.0    -580.5    895.7    .      • 

Mar.26  924     5.1     .     -      -  +4  42     2.0  56     913-8    +3  55  48.0    +68..0   893.9    -      • 

.746,  93038.3    7  29  24. 8  56  47  57. 8  56.047.3+4  634.1     -S63..    895.>     •      - 

Mar.26     94655.9.      .      ■  +44230.5  5625.0.4-^4  232.3     +241.8894.3.      . 

.746,  93436.673323.1  564957.0  561246.3     M  627.6-847.8895.0'.      . 

,  Mar.26     9  50  54.8    .      . 


17J9. 
Oct.  23     4  59  25.2 


+  4  42  35.4      56  26  54.1     +4     1   30.7    +296.9    896.3 


• 

220 

RESEARCIIKS  ON  THE  MOTION  Ol'  THE  MOON. 

riilnihtr  E 

\liilnt  of  Kctiiut'wn  of  lln-  On 

iiltiitioiis — Coiitiiuit'd, 

DELI.SI.E  AT  .ST.  PETERSHI;K( 

— Conliiuicc 

1. 

'osilion  of 
id  Slar. 

.\o. 

Star  (icculleil. 

1 

1 

Dale. 

i 

i  Local  mean  and 
Sidereal  Times. 

Greenwich  Mean 
Time. 

M<»on's  Tabular 

0 
'S   5 

■J      lA 

0    0 

.Apparent 
Mouii  A 

1 

/-/,          .S' 
t'-H         J) 

/ 

0 

^oni^iludes. 

I.alitiicles. 

1 

1 

245 

PI.  Pleio..  23  //,  I. 

h 

I74f),      10 

m       s     li    III       s         ° 
21   25.6    8  20  12.1       57 

1         n    ! 
13    22.5 

S<>  3*^  44-4 

.      1      " 
+  4     5     3.9 

M                                 ff                             O 

-797.fi     893,9     .        . 

•Mar.  2f)  III 

37   51-5    ...         +4 

43  33.2 

5fi  50     2.0 

+  3  58   18.2 

+  405.7     892.6 

24f, 

I'l.  Hessel   S,  I.     . 

1 74f'.       ') 

I   43.7    7     0  30,2      5(, 

33  30.3 

55  5f>  34. f' 

+4    7   17-9 

-877.7     895.8 

. 

Mar.  26    <) 

17  5fj-5    •      •      ■         +4 

41   54.4 

5'"  11    12,3 

+  4   10  31.3 

-193.4     896,5 

247 

I'l.  Hesse!  ,j,  I.    . 

I74<J.       'J 

2  2.S,4    7     I    14.9      Sfi 

33  52, fi 

55  5f'  5f'.3 

t-4     7   If).  7 

-802.2     895.8 

Mar.  2fi    0 

iS  41.3    ...         +4 

4'   55.3 

56  u   38.5 

+  410     fj .  0 

—  169.3     S96.O 

24S 

PI.  Ik-ssel   4,  I.    . 

1 74f'.       ') 

5   IS, 7    7     4     5-2      jf) 

35   I7.S 

55   5S   19." 

4-4     7   12.7 

-404.8     S95.7 

1 

: 

Mar.  2f)    9 

21   32.1     ...          (-4  41    58. S 

5f'     5     3.S 

+  4  20  33.1 

-800,4     896.5 

'  24') 

PI.  Hessel    10,  I. 

1 74<'>.       ') 

11   40,8    7   10  27.3      5O  3S  28.9 

5&     I  25.4 

+  4     7     3.7 

-815.6     S95.5 

Mar.  26    g 

27  55-2    ...         +4 

42     6.8 

5f'  15     i.o 

-t-4  13  20.9 

-377.2     896.6 

250 

PI.  Hessel    15,  I. 

"74^1.       'J 

28  2S.7    7  27   15.2      56  46  53,0 

5f'    9  42,8 

+  4     f>  37.7 

-877.5     895. ll 

( 

Mar.  26    0 

44  45-9    ...          14 

42  27.8 

56   2(   20.3 

-1-4     3  27. 8 

+  189.9     895.7 

251 

PI.  Hessel    iS,   I. 

1746.       y  =<)  44-4    7  28  30. (J      56 

47  30.9 

50  10  20.6    +4     f)  35.6 

-885.5     S95.I 

]         ! 

.Mar.  2f)    y 

If'     1.8    ..      .         +4 

42  29.4 

5fi  25     f).i    +4     3  57.5 

+  158.1     897.31 

i 

1 

252 

PI.  Bcssel    2<j,  I. 

I74f>.      "> 

9  20. 1    8     8     f).f)      57 

7   19.4 

5f)  30  26. S    +4     5  26.8 

-787.8     894.2 

( 

Mar.  26  10 

25  44.0    ...         +4  43   18.3 

56  43  34.6    +4  12  32.1 

-425.3     893.5 

i 

253 

PI.  Cel.,  16  i'.  I. 

1747.     '3 

I  4S.511     0  35.0      5f, 

23   11.7 

55  Ad  42.0    +4  33     5.9 

-464.3     892.5300.6 

' 

Jan.  20     9 

I   27.7    ...         +5 

6  42.3 

55  54  2f).3    +4  20  22.6 

+  763.3     892.7115.3 

254 

PI.  Tav.,  ly  ,-,   I. 

1747,     '3 

3  55.5  11     2  42.0      56 

24   14.f1 

55  47  42,2    +4  33      1-5 

-S70.5     892.5     .       .     i 

Jan,  20     9 

3  35-1     ...         +5 

f'  43.3 

5f)     2   12.7    +4  29  33.1 

+  208.4     892.5 

t 
1 

255 

PI.  .\st.,  21   /.:  1. 

17          13 

25     4.4  I'   23  5", 9      5(> 

34  43.3 

55  57  49-2    +4  32   14. S 

-894.4    883.6 

Jan.  20     9 

24  47.4    ...         +5 

6  52. f) 

?fi  12  43.6    +4  32  32.2 

-    17.4    891.8 

256 

I'l.  Mala,  20  ,,  I. 

1747.      >3 

2fi  21.5  11   25     8.0      56 

35  21.5 

55  5S  26...    +4  32   1 1.9 

-642.4    838.6 

. 

j  Jan.  20     9 

1 

2()     4.7     ..      .         +5 

f)  53.1 

5()     9     9,0    +4  21   51,8 

+  620.1    891.5 

257 

22  /,  I. 

,     1747.      13 

2S    21.511    27      8.0       56 

36  20,9 

55  59  24.5'   +4  32     7.2 

-890.4    891.8 

Jan,  20     9 

2S      5.1      ..        .            +5 

f'  54,0 

5f'  14   14.9 

-1-4  3"  33." 

-1-   94  .1    892 . 6 

25S 

PI.  Tay.,  ic,  e,  E. 

1747,      '3 

15    12.5  11    13    59.0       56 

0  54.0 

5f)  17   10.9 

+  4  27  3i'-7 

+  887.1    892.5127.4 

July  30  21 

47  5f'."     •      .      •         4-5 

14  49-9 

56     2  23.8 

+  4  29  30.3 

-119. 6    892.5288.6 

254 

PI.  Hessel   4,  IC.  . 

1747.     '3 

19  33.5  11   18  20.0      5f) 

3     3.3 

5f)  19  21.4 

-1-4  27  43,4 

+  783.5    892.6    .      .   j 

July  30  21 

52   17.8    ...         +5 

14  49-9 

5f'    f>  17.9 

+4  20  30.9 

+  432.5    892.9    .      .    j 

260 

PI.  Main,  20  r.  K. 

1747,     13 

26  37.5  11   25  24.0      56 

f>  33.4 

56  22  52.2 

4-4  28     4.5 

+  812.2    892.8    .      .    1 

July  30  21 

'                1 

59  23.0,   ...         +5 

14  50.0 

56    9  20.0 

+4  21  49.1 

+  375.4    892.6:    .      . 

! 

• 

RESEARCHES  ON  TIIK  MOTION  (JF  Till'.  MOON. 
lii/nilar  Jix/iihil  oj  lieiluclion  oj  the  Oiiitllali<>iis—(\mU\mi^<. 

FLAMSTI'.r'.l)  AT  CRKHNWICIl. 


22  1 


A|]p;irfnl    I'osilioii  of 
Moiiii  ;inil  Si. II. 


;  No,'  Slav  occiilU'il. 

261  C  Arirtis,  I.    . 

262  2S  (i,)  Ciem.,  I. 

!  363  !  K  A<|uarii,  E 

i 

I 

'  264  0  SiiKitlarii,  1. 

205  Mars,  I.     .      . 

266  Mars,  E.  .     . 


Dale. 


/■-/,  .'-'  0 

A- -A  /)       /.-© 


J    !^' 


l-oiigilmU'S.     I.atitmlcs. 


267 
268 


IT  SaRittarii,  I. 

Not  itlenlifit'il 
269'.  /)-'Sagiltarii,  1. 
270 '  Not  iileiilitied 

271  Lalaniit:  4()03 

272  "■  Cancri,  I.    . 

1     r        . 

273  a  Cancri,  b.  . 

274  "  'rami,  I 

! 

275  n  Taiiri,  E.    . 

276  "■  Taiiri,  I. 

277  (1  Taiiri,  E. 

278  ;   Tauri,  I. 


/(     m      s       h     HI    s 
l(,-li.       7   '''  21)        ...  47   5"     "-I 

Mar.  iS     7     4   ?7-'i    ...        +3     ')  S'-' 

1670,     13  17  3'J        •      •      •        ""  5"  4'-7 
Mar.23    13  2f]  4<'.7    ...         -24  28. 7 

Ifi7f),      II   3"  10        .      .      .        334  57  33" 
liiiiu2(j  IS     5  25.5    ...         +51   25.5 

1676,       8   lf>  4b        ...        2Sc)   13  24.'' 
Aug.  IiJ  iS   12  33.0    ...         +1   42  4''-2 

l07fi,      12    17  23  •      •  77  25  2().S 

Aug.  31  23     I     ')-2  .      .         +0     (}  26,0 

1676,     13   18   10        ...  77  55  2S.0 

AuK.31     i>     2     6.2    .      .      .      .   +0     0  4(1.4 

1676,  5  40  55        .      .      •        2S1   53  32.1) 
Nov.  9  20  59  35        ...        +2  jS  3(1.(1 

1677,  12   17     7        .      •      ■  fi4  3'J  5"-8 
Mar.  9   II  29  58-8    ...        +0  16  32.4 

1678,  7     6  32        ...        284  4')  3<).-l 
Sept. 24  19  22  10.0    ...        +4  48     9.2 

1678,       8  28  20        ...  ... 

Oct.  29 

1O78,       8  35  38        .      . 

On.  29  23    9  30.1    .     . 
1(180,     9    I  24      .     . 

Jan.  lO     4  45  50.8    .      . 

1680,     10     7     5  .      . 

Jan.  ifi     5  51  A-''>  ■ 

1680,     15     o  53 

Sept.  13     2  3()  28.7  . 

1680,     16     9  12 
Sept.  13     3  44  58.9    • 

1680,       7  50  43 
Nov.   7  23     I  58.(1    . 


1680,       8  47  12 
Nov.   7  23  58  36.9 

1682,       9  45  35 
Mar.  14    9  16  54.8 


47   1'   24-2 
47  25  29.3 

1  Id  22  111.7 
no  34  43.(1 

335  1"  54-<' 
334  S';  1-4. 
28(1   14   10.2 

280   2S    45.3 

77  55  41.3 
7S     9     0.4 

75  25    14.5 

78  I"  27.7 

281  29  45.2 

2,Sl    44   23.2 

64     o   i().9 

2S4  40  21.8 
2S4  56  15.' 


+  2  45    29. S  _    845.1     S92.835S.7 
+  2  51   45.7  -   375-')    ')24.o    48.7 

-2  50  21. 1  -   752.9    919.3      3-7 
-2  40  44.5-    i-('-<>    <)AT.('to(<.<) 

-t-4     '■  47.5   t-   952-f'    942.4    1)8.5 
+  4     7  45.'   -      57.5    95'.'J23fi.4 

4(1  45   54."-   875.1    974.8  147.3 
t-o  56  22.()—   (■)28.9  107S.4  133.2 

-d  32   5(1.(1—   71)9.1    892.6158.8 
-o  2S     0.4—   21/1.2    852.2279.4 

-o  32     7.(1  +   SS6.8    8()4.9    .      . 
-11  27   57.(1-    250.0    921.3    .      . 

+  1   35  29.5-   938."    985.5227.9 
+  1  28  47.9+   401.61020.0    53. S 

—  02041.4  .      .    893.9349.5 


+  3  53  35-7-  953.3   969.2  181. 8 
+  3  48  36.1  4-   21)9.6   ()97.2io3.i 


216.4 


37     3  53.8 
— o     o  59.0 

128   15   55.5 
-4  3'   28.3 

128  52     5.1 
-4  3"     4.9 

I     64   54  25.7 
-4  46  29.7 

65  35  10.8 
-4  48     6.0 

64  33  16.0 
-4  39  27.6 

65  9  12.5 
-4  40  47.7 

61  48  36.0 
-5  M  55-9 


7  17     2.7    -o  47     5.6 


37 

123  55  21.3 
129  10  50.5 

129  25     .1.0 
129  10  50.5: 

65     3  44-4 
65   19  48. 6 

65  34  37.4 
f,5   19  48.6 

65     2  37. 8; 
65  20    9.4; 

f,5  36  22.2 
65  20    9.4; 

61     5     4.0 
61  21  23.0 


980.7 


-5     1   19.4-   929.2    939.3296.8 
-5     6  20.1  +   300.7    973.2192.4 

-4  59  48.9+   853.5    940.8    .      . 
-5     6  20.1  +    391.2    935.9    .      . 

—  5  24     3.8—  (J64.2    986,3172.2 

—  5  29  22.1  +   31S.3  1011.2253.I 

-5  22  56.6  +  S88.S  986.8  .   . 

-5  29  22.1  +  3S5.5  965  I  .  .  : 

—  5  29  14.3—1051.61008,9226.3 

—  5  29  23.24-   8.91046.8198.8 

—  5    27   36.54-    972.8101 1.  2     . 
-5  29  23.2  +    106.7    97.(.S    .      . 

-5  ,(9  6.8-  979.8  957.7  354-8 
-5  46  4.3-  1S2.5  991.7  66.6 


I 


222 


RKSEARCMES  ON  Till-.  MOTION  OK  Till.  MOON. 
Tabular  Exlnhit  of  Reduclion  of  the  Oaultalioiis — (.U)ii('luilcil, 


I'L.VMSTEKl 

AT  ( 

iRKENWK' 

1  — ronliiiued 

] 
'an  and 
Times. 

i 

h  Mean 

i'aliular  j 

itric         1 
ion.          j 

1 

.Apparent   F'osliion  of 
Monn  and  Star. 

1  -1. 

i"     1     0 

No,       Slar  oceiilteil. 

Date.          ^  ^ 

.i   =           ■     S  .= 
S               Sua. 

1— 

. 

i/-n 

V      /.-0 

1       8  3 

ii 
0 

5  - 

Longitiules. 

EalilUflcs, 

■ 

! 

h    m      s 

//    m     ,1- 

279'  y  Taiiri,  E.     .      . 

l6S2,      ID  41    15 

62   21)  28.8 

61  31    0.3 

-5   5'   '5-5 

+S76.5 

055.7,354.8 

.Mar.  \\  to  12  .)3.(j 

i  -5  14  sh.?!  fji  2'  23.8 

1 

-5  4^1    4.3 

—311,2 

925.9   66.0 

380 

)■  Taiiri,  I.      .     . 

lfiS3,     II   57  41 

1 

61   51   25. i|     fii     ij  11,8 

-5  3^  41.8 

—  700,  s 

■ 

043.73I7.4  1 

' 

Veil.    5     ij     2  32.7 

-5     3  33.0      61   22  2-;. I 

[ 

-5   4f'     41 

+  5')2.3 

067 . 1  1 04 . 0 

281 

;    Tauri,  V..     . 

lf.83,      12  47  43 

j     f>3   10     7.1      '"   35  28-5 

-5  37  42.4 

+  786.4 

042.3    •      . 

Fell.    5     ()  52  42.y 

—  5      2   46.4        fll    22    22.  r 

--5  4''>     4-' 

+  501.7 

920.6    .     . 

382 

IK) Taiiri,  I.   .      . 

1683,       S  4(1  .(O 

,    V)  is  iy.3 

7S  43    0.3 

-4  3S  22.0 

-Oif'.7 

042.4    '3-3 

Apr.  2     ()  31  47.4 

-■)    3  42. f' 

78  5»  17.0 

-4  43  38.0 

+  315.7 

966.6   65.7 

283 

I  ig  Tauri,  V..  . 

16S3,       cj  27  54 

70  40  58. 4 

70    3  26, f) 

-4  33  55-4 

•i-ooo-'i 

Apr.  2    10  13     8.2 

-4     2  20.5 

73  58  17,0 

-4  43  33. (. 

+  283.2 

040.8    .     . 

284 

n  Leonis,  I.    . 

l6fc3,       ij  55  24 

' 

U5  25   17. f' 

145   "4     4" 

+  <)  30     I-O 

-7(17,2 

081.8   44,6 

May  4    12  46  52.4 

+  1   24     I.I 

145  25  51.2 

+  0  27  ifi.f) 

+  705 -3 

008,7  100. 3 

1285 

0  Ltonis,  v..  . 

1683,      K)  40  i6 

145  52  10  9 

145  37     71 

+  0  38  26.0 

+  fi75-0 

080.5    .      . 

i 

May  4    13  32  3'  9 

' 

+  1   26  17.7 

145  25  51.2 

+  0  27   I  (1.6 

+  M1O.4 

051.3    .      . 

1286 

Jupiter,  1.       .      . 

16S6,       y  33  33 
Apr.  10     .      .      , 

. 

.      .      . 

.      .    21. .t 

287 

Jupiter,  E. 

16S6,     10  32  38 
Apr.  10     .      .      . 

' 

•      • 

.... 

24B:  Saturn       .      .      . 

1687,     13  30  37 

Mar,  28     .      .      . 

' 

.      .      . 

•      •      • 

•     • 

.      -,     8.4 

RKSEARciir.s  ON  tup:  motion  or  thl:  moon.  223 

KCilJATIONH  OK  CONDITION  OIVEN  HY  THI-}  l»l{i:(!i:i)IN(}  OCCULTATIONS  OK  STAKH. 

We  may  coiisiilcr  it  useless  to  attoiiipt  to  determine  trnin  these  nldcr  (iltHcrviitions 
any  oluiiieiitM  oi'  tlio  inoou's  orl)it  wliicli  r*;iniiin  eoiistiitit,  and  wliirli,  tlKU'et'ore,  ciin  lie 
(letennined  for  any  time  t'nnii  recent  uliservatinns  aioiie.  Snch  are  tlie  moon's  ecceii- 
tricity,  iiudination,  semi-iliumeter,  and  parallax.  Hut  it  may  lie  ad\  isalile  to  introduce 
the  corroctious  of  those  last  two  ohiuients  intc  the  eijuatious,  in  order  that  when  defin- 
itivo  nuxhu'ii  values  are  <il)taiii(Ml,  the  cupiations  may  l)(3  corrected  accordiuf^ly.  it  is 
otherwise  with  the  lonj^itudes  of  the  node  and  of  the  periiu'ee,  because  the  variations 
of  these  ([uantititis  have  to  lie  detc^rmined  from  oiiservafions,  and  the  epoch  of  the 
observations  now  under  considciration  is  so  nnnli  more  remote  than  that  of  the  obser- 
vations used  by  Hanskn,  that  we  may  expect  them  to  irive  j>dod  results  for  the  values 
of  the  variations  in  (piestion.  'riie  most  imjiortant  elenumt  to  be  det(;rmined  is  the 
correction  to  the  moon's  mean  loni^itnde,  and  it  is  to  this  that  our  attention  will  be 
principally  devoted. 

The  only  elements  whi(di  we  shall  attempt  to  determine  at  the  jiresent  tini>  'vre 
the  corrections  to  the  inooi\'s  mean  lonji'itn<le  and  lonj^itude  of  the  node,  the.se  In  i^;- 
the  only  ones  the  admissibh;  alterations  in  wiiicli  can  materially  alti.'r  the  conclusions 
to  be  drawn  from  tlu^  accounts  of  ancient  eclipses,  'i'he  correction  to  IIanskn's  motion 
of  the  }ierijfee  is  probably  very  small,  and  any  value  of  it  which  could  be  deduced  at 
present  would  be  only  |)rovisional.  We  shall  therefore'  present  the  er|nations  of  con 
dition  in  such  a  form  that  tlwy  can  be  hereafter  delinitively  resolved  with  improved 
data,  when  the  latter  are  available. 

Errors  to  ivhUh  the  n/tiatioiis  arc  tialtlr. — These  may  be  divided  into  two  classes; 
(a)  tho.se  of  pin-e  observation,  and  (/i)  those  of  the  elements  of  reduction. 

(a)  The  errors  of  pure  id)servation  resolve  themselves  almo.st  entirely  into  errors 
in  the  determination  of  the  time,  provided  that  the  instantaneous  immersion  or  em«r- 
sion  of  the  star  is  actiudly  observed.  In  the  case  of  innnersions  at  the  dark  limb,  this 
can  not  be  a  subject  of  doubt;  but  in  the  case  of  the  other  three  cla.sses  of  phenomena, 
more  or  less  doubt  or  suspicion  niay  exist,  according'  to  circumstances.  In  tluf  case  of 
the  brif>'hter  stars,  snch  as  Aldebaran  and  S])ica,  and,  indeed,  from  the  year  1680 
onward,  in  the  case  of  all  stars  bri;i'hter  than  the  fourth  maj^nitmle,  no  distinction  of 
bright  or  thirk  limb  need  be  made,  because  siu-h  stars  can  be  readily  seen  at  the  brijiht 
limb  with  telescopes  of  moderate  optical  power.  Observations  of  smaller  stars  at  the 
bright  limb  are  to  be  looked  on  with  snspicion,  and  rejected  entirely  if  there  is  no 
special  reason  to  believe  them  accurate.  All  emersions  are  to  be  received  with  sus- 
picion, owing  to  the  doubt  whether  the  observer  sa^v  the  star  at  the  moment  of  its 
reapi)earance.  They  should  be  retained  only  when  tlu;re  is  reason  to  believe  that  the 
observer  did  not  record  as  gooil  an  observation  which  failed  in  this  way. 

Besides  these  errors  of  observation,  there  may  be  a  jiersonal  error  of  a  fraction 
of  a  second  in  estimating  the  tinie,  which  will  necessarily  elude  discussion,  and  which, 
therefore,  need  not  be  farther  considered. 

(/5)  The  errors  in  the  elements  may  be  divided  into  three  classes:  (i)tho.soof 
the  lunar  theory;  (2)  those  arising  from  deviations  of  the  moon  from  a  spherical  form; 
(3)  those  of  the  adopted  po.sition  of  the  occulted  star. 


RKSKARCIIES  ON  Tllli  MOTION  OF  THE  MOON. 


(I  )  III  I'iirl  III  ut'  I'jipm's  piililislicd  liy  tlic 'Priuisit  of  N'fiiiis  (Juiumissiiin,  jicriodic 
cMiTcc'tioiis  to  II.wsi.n's  'riicory  (irc!  (iciliicdd.  of  wliifh  tlio  iiicaii  vjiliu'  will  .sonit'wliat 
cxcouil  one  second.      .Mr.  Ni:i.><on  Ims  found  ii  term  prodiicod  Ity  tliu  iiction  of  .Jiipitor, 

tliciriit.      Oflici'  terms,   still   unknown,  niiiy   luirciiftcr  I 


)e 


which  liJis  fi  yet  liirjicr  coi 

discovered.      .Mtooetiier,  I  tliiiilv  the  proiiahle  error  of   II.W.skn's  'I'lieorv,  leiivinj''  out 


terms  ot   ioiiji'  |ieriod,  may  he  estiniati'd  at  2   . 

(2)   I  am  not  aware  of  any  investii^atioii   iiavin;;'  for  its  oiiject  to  (h'toniiiiio  the 
deviations  of  tlie  moon  from  a  spJKM'ieal  liniin!  as  alfectin;;'  the  time  of  an  occiiltati 


on. 


lie  proiiahn^  iiiai'' 


'•nitinli-  of  tiiis  deviation  is,  I  think,  less  tiian  i' 


roll' 


(3)  Tlio  pi'oltaitle  errors  in  the  coinpnted  positions  of  the  occulted  stars  may  1 
iiilv  estimated  at  2"  in  tlie  case  of  stars  well  ol)serve(l  liv  Hkadlkv,  and  at  a  val 


)C 


lie 


•<till  "renter  in  tlie  case  of  stars  not  so  oltserved. 


)f  th 


Leaviii^i'  out  errors  of  (di.servatioii,  I  conceive  that  the  ininiimim   prohahle  (MTor 


lite 


line  of  the  disti 


hotv 


tlio  star  and  th 


.f  th 


twt'on 

{!>)  can  hardly  he  less  than  _V'  'n  fhe  most  t"a\dral»le  i-ascis,  and  may  he  {freiitcr  to 
anv  extent  in  niifavorahle  ones.  \\'lieii  in  the  (roiirse  of  time  the  lunar  theory  is 
pcM'fected,  and  the  proper  motions  of  the  stars  are  lietter  determined,  this  prohahlo 
ei'ror  may  he  considerahly  diminished. 

\Vlieiie\'  there  was  any  means  of  estimating  the  pndiahle  error  of  tlu*  timo,  that 
estimate  is  j^iscii  in  the  following'  list  of  eipiatioiis  in  the  c(diiinn  :^t.  Its  etl'eci  is  to 
1)(!  included  in  estiinatinn'  the  prohahle  error.  To  eiiahle  this  to  he  done,  the  (dianf>'e 
of  Ii  ill  one  second  of  time  is  included  in  the  eipiatioiis  of  condition.  Tlie  sij.;'nifi- 
cations  of  tin*  indoteriiiinato  (|Uantitiu.s  in  the  eipiation.s  are  as  follows: — 

fit,    the  correction  to  IEansion's  mean  loiij;itude  of  the  moon  at  the  date. 

'5/,    the  correction  to  the  <d»served  time,  should  any  he  necessary. 

I^w,  the  correction  to  the  lon<>itii(le  of  peri<,''ee. 

<^0,  the  correction  to  the  loiif^itnde  of  node.  •  ^ 

'W;,,,  the  correction  to  the  moon's  latitude. 

A//,  the  correction  to  the  moon's  parallax. 

The  mode  of  computing  the  coefficients  of  these  (puuitities  ha.s  already  heen 
descriheil  in  §  6,  jiages  55  to  6S. 

The  ahsohite  tctrms  of  the  e(|natious  are  tin  values  of  l>—S',  formed  from  the 
projier  coluimi  in  the  exhiliit  of  reductions  already  <;iven. 

In  colinnn  ±  *  i*^  f^iven  the  .supposed  prohahle  error  of  the  observed  times,  (»rthe 
prohahle  order  of  inagnitnde  of  ^^t.  In  the  observations  of  Cassini,  Series  II,  it  may 
he  assumed  that  the  jirobahle  error  is  always  about  2"  or  3". 

The  phase  (immersion  or  emersion)  and  the  limb  (bri<>'ht  or  dark)  are  indicated 
only  in  the  unfavorable  ca.ses,  blank  signifyin<^-  an  immersion  or  a  phencmienon  at  the 
dark  limb,  while  E  indicates  an  emersion,  ami  \\  the  bright  limb. 

After  the  time  of  IlEvi'.Lirs,  the  jirobable  errors  of  the  equations  ari.se  almost 
entirely  from  the  uncertainties  ie  the  jiositions  of  the  stars  and  the  periodic  inequali- 
ties of  the  moon,  and  are  but  slightl)'  increased  by  the  probable  errors  of  the  observed 
times.  In  the  case  of  these  obser>ations,  the  last  column  shows  the  relative  weights 
which  have  been  assigned  in  the  provisional  solutions  of  the  ecjuations. 


KKSKARfllKS  ON    llli:  MOTION  ol   Tllli  MooN. 


225 


mi.l.lALDUi). 


lll'A'r.l.irS-rcmliniicil. 


l'.i|ii;iliiin. 


ii'  Ycnr,     i    4 


F.ciii 


0.031! 

■  o.c)3 
o.So 


().23iW  -  7i)-l  !  •     lf'35'0> 

-  0.47       +105. (j     .     i63i).3 

-  o.4»       +  10.7     .  i  1641.3 


CASSKNDI^S. 


I 


5.0  = 
j    f)    o  - 

i    7  0  = 

I    8  o  - 

I  »<j  o  - 

i  to  o  — 

)  1 1    o  = 

I  12    O  - 

13  o  - 

i  14  o  — 

I  15  o  = 

i  16  o  = 


o.83(l- 

o.cjl 

o.5() 

0.38 

o.7<) 
■  1.07 
•0.33 

0.62 

-  I  .03 

-  o.()8 

-  o.(jS 

-  l.oS 


-  o.jOfW  +   34.''i 

—  0 


—  o. 
+  ". 

—  o. 

—  o. 

—  o. 

—  o. 

—  o. 

—  o 

—  (>, 

—  o 


41 

21 

I') 

27 

5S 

45 
31} 
60 

3S 
27 
54 


+  O2.4 
(■   17.5 

+  3-8 
-MSfj.o 

+  10(|,(j 

+  57-4 
4-  41.3 
+   Sf,.'' 

+  47.0 
+  f>.8 
-  50. 8 


! 1627.5 1  . 
1 1627.7'  . 
'  1632.1 1 . 


1635. 

l637- 


163?. 
1631}. 


17  o 

18  o 
I  ig   o 

i  20  o 

1 

I  22 

i24 
^25 
126 

127 


:28 

'29 


—  1.07" 
+  1.04 

—  1 .  10 

+  I. II 

—  0.51) 

+  0.()2 

—  o.3i 

:  -  0.83 
:  —  I.Oq 
:  —  I . 02 
:  —  0.65 
:    +  0.66 


iir.vKLirs. 


I 

f  -0.47,1/  +   57-3    35    i^'44- 

+  0.48  -   3'J.''   35 

-  0.47  +   17.5    35    If'-t5. 
+  o.4()  -   30.9'  35 

—  0.30  +   53-5    25    ifisS- 
+  0.3S  -    25.0    12    1660. 

—  0.37  +     6  6    20    1660. 

-  0.45  +   3S.I    40    I^'i3- 

-  0.58  +105. 5    25 
-0.56  +   53-1    25 

—  0.27  +     II.O     12     1663, 
+  0.26  +       3.2     12 


^The  final  revision  of  tlie  ohsciv 


30  o  =  —  1.031W 

31  ()  rr    +  o,l)7 

35  o  —  —  0.86 

36  o  =  +  0.71 

37  o  =  —  i.o<i 

38  o  =  -  1.14 
31)  o  =  —  1 .  00 

40  o  =   —  o .  6() 

41  o  =  —  0.77 

42  o  =  —  o.8g 

43  o  =  -  0.81 

44  o  =  -  o.i)6 
E     H     45   0  =  -  "27 

4f,   o  =--  -  0.7S 

47  o  =  +  0.37 

48  o  —  —  0.18 

49  O   =    +  0.()0 

50  o  —  —  o.yl 

51  o  -  -  0.36 

52  o  -  +  0.55 
Ij  53  o  =  -t-  0.70 
55   o  =  -  0.57 

57  o  =  +  0.52 

58  o  =  —  0.88 
5<j  o  =  +  o.cio 
62  o  ~  —  0.8S 

—   63:0  =  -  O.S3 

B      64  O  =   —  O.QI 

65  o  =  4-  0.86 

M     66  o  =  +  o.Si) 

61)  o  --   —  0.56 

H     70  o  ^  +  0.55 

.      71  o  --  —  1.13 

73    O   _    +    I.0() 

•      73   "  ~  —  '-OS 

.      74   o  -  -)-  1.04 

.       .      75   o  -^   -  1. 00 

.      H     76   o  i-  —  o.()6 

K      .      77   o  -  +  o.i)5 

ilions  for  lime  indicate 


E 

8     . 
3    E 

5     • 


nation. 

±f     Yrar.      i     1 

_^..          !-«-*' 

-  C1.541W 

+   37.4 

.r 

18     1 664..'      .        . 

+  ".57 

-  15.4 

18                    E     M 

-".34 

4-   21).  3 

15    "'71    3      •       • 

t-  0.34 

-   23.4:15         •■         !■■     " 

-  0.43 

(-   51 .7  '  30    1672. S     .      H 

-  0.48 

+   48. 8    28         "          .      » 

-  0.41 

+  53') 

25         •■          ■      H 

-  0.36 

+   11.2 

25    1673-2     .       . 

-  o.3<; 

1    33.3   25        "         •   1  • 

-  0.48 

-f-  15.4   25        "         •      • 

-  0.44 

+  23.1    25        " 

-  0.45 

+  .19. <)   2ii    1674.6     .     H 

-  0.18 

+  25-3   25                  •     1* 

-  ".35 

+  40.8:25        ■'         ■     I' 

+  o.n 

+     3-9   25        "        •■•      • 

—  0. 13 

4-   12.8   25         "          ■     H 

+  0.42 

+34.125        "        E      . 

-  0.3S 

t-  26.2   25        "              li 

—  0. 11 

-     7.7    25        •■        E      . 

+  0.27 

-   14.8   25        "        f-     • 

+  0.36 

-  23.1   25        "        E     . 

—  0.2.1 

+   10. 0   3')    1675  ■'>     •      •   1 

+  0.24 

-     1.8    30        "        I^      • 

-  0.45 

4-  46.3    iS    1676.7     .     H 

+  0.41 

-   18.8  1 20        •■        E      . 

—  0.40 

—  25.4    72    1673.2     . 

-  0.35 

-^-  15.3   22    1670.2     .     U 

-  0.36 

4-   12. 1    20        ''         •     H 

+  0.36 

+     4.3    15        •■        E      . 

+  0.38 

-   24.4    16         "         E      . 

—  0.24 

+   19.4    6?    1679.5     .   ,  B 

4-  0.22 

1    II. 3   6?        ■■        E  1  . 

-  0.43 

+  54.6   20   16S1.0     . 

+  0.47 

-     1.5    17         ■■         '■;     » 

-  0.44 

-t-    57.4      S    1683.0     .       . 

+  0.44 

-  39-3      8         "         E     U 

)      -0.53 

4.146.5    25    1683.3     .       .  ■ 

)      -0.54 

-r    9S.I     22           "            .        . 

+  0.56 

—   59.6   2''         "        E     M 

e  a  vahic  0 

f,(/=4- I43''-                                  1 

20- 


75  Ap.  2 


226 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


CASSINI  AND  OTHERS, 


8 

a 
'A 


78 
80 
81 
85 
86 
87 
88 
92 


93 
94 
95 
96 

97 

93 


E<iiiation. 


o  =    -  o.gO(!f  —  0.3S1W  —  1 .93t'(l 

o  =  —  0.82  —  0.3S  +0.91 

0=4-0.97  +0.37  —1.09 

0=  — 0.72  —0.40  +0.23 

o=  — 0.32  —0.18  —0.45 

0=  +  o.i8  +0.16  -1-0.66 

o=  — 0.76  —0.39  —1. 13 

o  =  —  1 .03  —  0.51)  +  1  .Oi 


o.oo((W(  —  o.oi  (i/'u  +  o.32(i  II  4-  23.  r 


+  o.ii 
+  o.oS 
—  0.22 
+  0,94 
+  0.86 
+  0.09 
4-0.15 


■  0.68 
4-  0.49 
4-  0.71 

-  0.95 

-  0.87 

-  O.rO 
-0.35 


-0.83 
4-  0.13 

4-  0.18 
4-  0.37 
4-  0.56 
4-  0.81 
-  0.13 


+  31.7 
-36.6 
+  19.5 
4-  12.7 
-  7.6 
4-  19.5 
4-  16.0 


±E 


0? 
10? 

10? 

2 

3 

3? 
5 
3? 


Year. 

1 

1672.6 

1676.2 

" 

E 

1683.1 

1685.0 

. 

.. 

E 

16S6.5 

1690.5 

LA   HIRE. 


99*  o  = 

100  o  = 

101  |o  = 

104      ;       O      := 


-  1.07, 

-  1.04 
—      0.32 

4-  0.4S 

—  0.90 

—  0.60 

+  0.73 
-0.57 
4-  0.53 

—  0.60 


k  —  0.421'/  4-  1. 52 I'll  3      o.oo/i!f(  —  0.08 (Sfco  4-  o.23(in  4-  34.9 

—  0.41  4-  1.47  0.00  +  0.27  4-  0.10 

—  o.:3  —0.45  4-0.94  —0.95  4-  0.J7 
4-0.16  ■(-0.66  4-0.86  —0.87  -t-o.sO 

—  0.50  —2.00  —  o  o3  4-0.08  —0.63 

—  0.36  4- o.>jD  -0.2S  —  0.S4  4-0.33 
-H  0.30  —1. 16  —0.24  —0.74  4-0.85 

—  0.22  —  0.C2  —0.30  4-0.81  —0.14 
4-0.21  4- o. '3  —0.32  4-0.84  —0.79 

—  0.24  —1.30  4-0.76  4-0.76  —0.83 


+  34.9 

2 

4-  28.0 

2 

4-  12.8 

1 

-     7.9 

I    1 

4-  21.4 

2    i 

4-  17.0 

2 

—  19.0 

2    < 

4-     8.2 

2 

-  11.4 

2 

4-    3-2 

^ 

1682. I 


1685.0 

" 

E    , 

1685.8 

. 

1699.6 

.     j 

" 

E 

I70I.7 

" 

E 

I7I8.7 

• 

B 
B 

i    B 


CASSINI,  ETC.— SERIES  II. 


105 
106 
107 
loS 
109 
110 


o  =  —  o.75(!f 

0  =  -  0.95 

0  =  4-  l.oi       4-  0.44 

0=r    -  0.74  -   0.33 

o  =  —  0.83      —  0.31 
o  =  -  0.77      —  0.27 


o.40ri/4-   I.l6.-i(rj  —  0.2l/(lW  —  o.76ii/io  4-  0.991!  IT  4-  22.9 

0.43       4-  r.6o         -1-0.07  —0.59         4-0.77       4-23.3 

-1.86         4-0.04  —0.34         —0.23       —20.3 

40.82  —0.68  -h  0.70  +  O.IC)        —40.0 

—  0.52         4-0.21  —0.55         4-0.31       4-  2T.8 

—  0.97         —O.oS  —  0.5S         4-0.32       4-21.8 


Tliese  six  equations  result  from  using  Cassini's  correction  to  the  (|uadrant,  which  is  probahly  incorrect, 
following  these  equations  are  given  as  lesulling  from  the  new  correction. 

-  0.76 

-  0.59 

-  0.34 
4-  0.70 
4-  1. 01 
4   i.oi 


III 
112  . 

113 ! 

•14 

115 

tl6 
117 
118 
119 
120 
121 
122 
123 


0=  -  0.75 
0=  -  0.95 
0=  -(-  1. 01 

0=  -  0.74 

0=4-  0.01 
o  j=  4-  0.03 
0  -=  4-  0.30 
o  =  —  0.82 
o  =  —  0.76 
0-=  +  0.49 
c.  =  —  0.46 
o  =  —  1.05 
0.-=  —  1.05 


—  0.40 

—  0.43 

4-  0.44 

—  0.33 

—  0.02 

—  0.01 
■f-  O  .  I  1 

—  0.30 

—  0.27 

4  0.2S 

—  0.13 

—  0.43 

—  0.56 


■i-  1.16 
4-  1 .  60 

-  1.86 
4-  0.82 

-  O.OI 

-  0.04 

-  0.33 

-  0.50 

-  0.95 
-(-  0.62 

-  0.98 
4-  1.81 
4-  1.84 


-  0.21 

4-  0.07 
4-  0.04 

-  0.63 

-  o.gS 

-  0.98 

-  0.94 
+  0.21 

-  0.0" 

-  0.13 

-  0.85 

-  0.41 
4-  0.36 


+   0.96 
~  0.55 

-  0.59 

-  0.36 

-  0.87 
4-  0.41 

-  0.33 


4-  0.99 
4-  0.77 

-  0.23 
4-  0.19 

-  0.39 

-  0.41 

-  0.57 
4-  0.31 
4-  0.32 
4-  0.46 
4-  0.62 
4-  0.39 
4-  0.99 


1705.6 
1705.7 

« 

B   ! 

■' 

E 

B 

1 706 . 1 

1706.3 

, 

In  the 


*  Cassini's  recoril  is  10"  earlier  than  La  Hiuk's. 


-r  14. 1 

1705.6 

. 

B 

4-  17.5 

1705.7 

-  14.1 

E 

B 

-  469 

1 706 . 1 

. 

-  12.7 

-  13. 1 

" 

-t-  15.6 

" 

E 

B 

4-  16.4 

" 

+  15.7 

1706.3 

-    9.7 

" 

E 

B 

1-     7.5 

1706.4 

4    17.2 

1706.9 

+     9.9 

1707.3 

7«  in  solv 

"/■ 

;  t 

lis  e(|ual 

on. 

ll 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


227 


CASSINI 

ETC.— SERIES  11— Continued. 

umber. 

1 

E( 

lu.ition. 

Year.    '    2 

:  £  ; 

i 

i 

i  \ 

1    ^     \ 

1 

1 

124       0  =  —  0.52(W 

—  0 . 2 1  rl  /  —  I  .  1  ()  <•  li  :. 

—  o.5fj/ii« 

-  0.821WV 

4-  o.Sg'-ll  4-   15-7  j 

1707.7 

■      1 
_^    1 

1 
i  i 

125       0  =:  +  0.56 

+  0.23     +  1.14 

-  0.53 

-  0.78 

4-  0.59        —      6.3  : 

'    E 

B   1 

I 

1 

126    1    0  =  —  0.94 

—  0.50      +  0.26 

4-  0.38 

-  0.33 

-+•  0.99        4-    13-7  ' 

1708. I  j     . 

U  1 

127    1 

0  =  -0.93 

—  0.50       4-  0.25 

4-  0.38 

-  0.38 

4-  1. 00        4-      7-4 

" 

s 

128 : 

0  =  +  1. 01 

4-  0.61        —  1 .44 

4-012 

—  0.27 

4-0.65        4-    84.1  1 

1708.7       E 

0  ' 

.2q' 

0  =    -  0.33 

-  0.39       +  r.3( 

4-0.66 

4-  0.66 

—  0.74        4-    17-2  1 

1709-3    :        • 

• 

t  \ 
1 

1  130  i 

0=  -  0.50 

—  0.30      —  1.32 

4-  0.75 

—  0.7O 

4-  0.57        4-177-2 

1709.7    ■        . 

0 

.3.' 

0  =  -  0.S6 

-0.54      -0.03 

4-  o.u 

—  o.^6 

4-  0.05        4-,    7-3  ' 

V, 

i 

1 

1     '32 

0=  —  0.30 

—  0.22       —  O.OI 

4-  0.23 

-  0.95 

-h  0.71        4-    10.6  . 

V, 

i   I 

133  ; 

0  =  —  0.3c 

—  0.26       —  0.01 

4-  0.22 

-•  0.93 

4-  0.65        4-    17-8  ! 

" 

B 

'   ' 

134 

0  =  +  0.50 

+  0.25         +  O.OI 

(-  0.21 

-  0.S6 

4-0.96       —     4-0  i 

E 

0  ! 

'35 

0  =  +  o.i)3 

+  0  52       +  0.02 

4-  0.07 

—  0.29 

4-  0.63        -      1.3  1       "               ^ 

0 

136 

0  =  —  0.91 

—  0.50      —1.56 

4-  0  03 

4-  0.23 

—  0.65        4-    10.4  1 

1710.9        . 

I 

1    >37  : 

0  =  —  0 .  40 

—  0.2f)        —  O.O7 

-  0.14 

—  0.91 

4-  0.47        4-    ij-o 

"         1 

t 

I 

138 

0  =  —  0.05 

-  o.oS       —  0.08 

-  0.16 

—  I  .o<j 

—  0.7-        +    10.2  i 

'      . 

I 

139 

0  =  +  0.32 

+  o.i[       +  0.55 

-  0.15 

-  0.94 

-+-  0.33         4-    12. 1 

E 

li 

0 

'    140 

0  =  +  0.92 

4-0.44       +  '  •5'' 

—   O.OI 

-  0.17 

4-  0.56        4-    13-0  ■ 

E 

B 

0  1 

141 

0=  -  0.79 

-  0.31       -  i.7(> 

—   O.JI 

-  0.50 

4-  0.39        4-    17-5  . 

1711.7 

B 

i    i 

142 

0  =  —  0.20 

—  o.O(j       -  0.44 

—  0.42 

-  0.99 

4-  0.44         t-    12.6 

" 

B 

*   i 

143 

0=  —  0.48 

-  0.18       —  1.06 

4-0.33 

-h  0.36 

—  o.II        4-     S.I 

:      • 

B 

i  1 

144 

0=  +  0.81 

+  0.32       4-  1.80 

-   O.l'i 

—  0.46 

—  0.20        4-      7-8 

1     E 

0  , 

145 

0=  +  0.48 

4-  0.19       4-  I.oS"> 

4-  <'.33 

4-  0.85 

—  0.60        ~     6.3 

E 

0 

146 

0  =  -  n.56 

—  0.30       4-  0..;, 

4-  0.39 

4-0. 84 

-  0.68       4-    ii.S 

1712.4 

I 

147 

0  =  +  0.6O 

4-0.28       -0.17 

-    0.35 

4-  0.77 

-0.85        -     4-1 

E 

B 

0   1 

1 

148 

o=»-  0.93 

—  0.50       —  0.2G 

4-  0.31 

4-  0.32 

t-  0.41        4-    12. 1 

1714-2 

I 
,       i 

149 

0=  —  0.98 

—  0.40       —  1. 16 

-h  0.26 

—  0.30 

-^-  0.06      4-  18.0 

1714-3 

••        1     E   1 

B 

' 

r  150 

0=  +  0.98 

-h  0.39       —  I. 17 

4-  0.28 

-  0.32 

■y  0.34         -    14-9 

■ 

I 

1          " 

151 

0=  -  0.87 

-  0.33       4-1.56 

4-  0.48 

4-  0.60 

-  0.46        4-    13-9 

1715.6 

•       j 

B 

I 

152 

0=  +  0.O7 

4-0.32       -  '■") 

4-  0.65 

4-  0.80 

—  0.60        4-     4-2 

E 

■ 

0 

!     '57 

0=  —  0.56 

-  0.27       4-  0.64 

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tliSEARCHES  ON  THE  MOTION  OF  THE  MOON. 


CASSINI,  ETC.— 

SERIES  II— 

ContiiuKHl. 

s 

3 

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209 

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RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


229 


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2  30 


RESEARCHES  ON  THE   MUTION  OF  THE  MOON. 


FLAMSTEED. 


Si 
E 
s 
2 


Et|LKiti()n. 


2fc: 
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263 
264 
265 

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267  I 
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272 
273 
274 

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276  I 

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0  = 

280 

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0.38 

0.25 

0-77 
•0.64 


+ 


Year. 

6 

VI 

0, 

Limb. 

0.S4I 

11  +   31.2 

1676.2 

t 

0.90 

+   28.3 

" 

I 

0.29 

+     9-5 

1676.5 

E 

. 

0 

0-55 

+  103.6 

1676.6 

. 

0 

0.25 

-  40-4 

1676.7 

B 

0 

0.72 

+   26.4 

" 

E 

0 

0.03 

+  34-5 

1676.8 

. 

I 

0.13 

+  28.0 

1678.7 

. 

. 

I 

o.So 

+  33.9 

1680.0 

B 

I 

0.33 

-     4-9 

E 

. 

0 

0.35 

+   24.9 

1680.7 

B 

t 

0.24 

-   21.7 

E 

• 

I 

0.49 

+   37.9 

1 680 . 9 

. 

B 

I 

0.36 

-  30-4 

" 

E 

t 

0,84 

+   34-0 

1682.2 

t 

0.51 

-   29.8 

E 

B 

0 

0.26 

+   23.4 

1683.1 

I 

'•'■97 

-  12-7 

'■ 

E 

B 

0 

0.39 

+   24.2 

1683.3 

• 

I 

0.82 

+     8.6 

" 

E 

B 

0 

0.40 

+    16.9 

" 

. 

. 

I 

0.75 

—  29.2 

" 

E   ! 
1 

B   , 

0 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


231 


PROVISIONAL    SOLirTION    OF    THE    PRECEDING    EQUATIONS. 

Observations  of  Bn.LiALDrs  ami  Gassendus. 

The  only  quantity  which  can  bo  obtained  fn.ui  tliese  observations  is  a  rough  nicau 
correction  to' the  moon's  mean  h^i-ituih^  All  the  observations  used  were  immersions 
at  the  .hirk  limb,  except  in  the  case  of  the  comparativel>-  bri-ht  star  /*  Gemuiorum,  ot 
which  the  immersion  was  observed  when  the  moon  was  full.  The  principal  error  to 
be  feared  is  therefore  in  the  determination  of  the  time,  which  was  derived  by  observin<r 
an  altitude  at  the  moment  of  the  phenomenon.     The  probable  error  of  each  eciuation 

will  be  nearly  proportional  to  "^j^,  and  this,  a-ain,  is  nearly  proportional  to  the  cocfHcient 
of  8e.  Hence,  if  we  derive  separate  values  ..f  6e  from  each  equation,  the  results  will 
be  entitled  tonoarlve.pial  wei-ht,  supposing  the  times  determine-l  withe<iual  precision.^ 
In  combiuin-  the  ol)servations,  however,  I  have,  for  an  obvious  reason,  given  only  halt 
weight  when  the  object  whose  altitude  was  observed  was  less  than  two  hours  from  the 
meH.liau,  and  also  'to  the  confusi^.l  observation  of  ;/  Capricorni,  on  1635,  August  26. 
I  have  also  given  onlv  weight  i^  to  each  of  the  three  observations  by  BiLMAi.i.rs 
which  were  not  iiopelessly  erroneous.  ObserNations  at  the  bright  limb  are  passed  over 
without  remark.  The  last  observation  is  rejected  entirel\-  on  account  of  discordance, 
and  douljt  respecting  place  of  observation. 

The  separate  results  thus  obtained  are:— 


Wt.  =  \ 
d 

Wt.  ~  I 

4 


1635.0  '5£  =:—  125" 

39.3  +"4 

41-3  +    13^^ 
1627.5              <5i=r+    41" 

27.7  +    69 

32.1  +  29 
35.7  +  148 

37.2  +  102 
37.2  +  69 
37.2  +  68 
37.2  +  85 
38.1  +  48 
3S.1  +     10 

The  mean  result  is : — 

Epoch,  1635.7:    <5e  =  +  57"±9";    '5f'=  +  3-8". 

The  quantity  '^e'  here  represents  the  mean  correction  when  Hansen's  empirical 

term  is  removed. 

Obscrrations  of  Hevelius. 

The  treatment  of  the  immersions  ol)served  by  Henelius  does  not  oiler  any  serious 
difHculty;  but  the  fre.piency  of  cases  in  which  it  is  clenr  tVoiu  the  result  that  the  eniei- 
sion  was  observed  too  late  renders  the  use  of  the  (miersions  doubttul.  W  e  shall  divi.lo 
the  observations  into  gr.mps,  so  as  to  obtain  .-.orrections  for  vari.ms  mean  epochs. 


i 
I 

I 

I 

I 

I 

1 


232  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Group,  1644-1645. — The  two  occiilttitioiis  of  a  Tiiuri  o'ivc  very  satist'iictorily: — 

Ei)Ocli,  1645.2:   '5t=:  +  33".6;   ''>*' rr  +  12"  ±S". 

(li(iii[>,  165S-64. — 'Pile  ciiuTsiou  of  fi  Scoi'])!!,  1660.  A))!'!!  26,  Hevelus  coiiMid- 
orod  w(!ll  obsorvcd,  niid  the  result  seems  i;-ood.  The  other  two  oiiiersions  I  reject. 
The  result  thus  o1)tin"ned  is: — 

El)Ocli,   1662.0:    AV  ::r:-f.3S"  ±4";    f?^'  — 4-lS". 

(h-oiip,  1671-75. — The  iuniiersioiis  arc  nil  used,  althouj^'h  the  oecultiitious  of  the 
I'leiiules  011  1674,  .Vujiiist  23,  were  observed  at  the  hrinht  limh.  1  jud^c  from  the  obser- 
vatious  and  other  eousideratious  that  l[i;vi':i,irs  could  follow  the  stars  of  the  iMi;iades 
elose  up  to  the  liudi  of  tlu-  nioou.     The  emersions  are  all  rejected,     'i'lie  results  are: 

Kpoch,  1673.9:   '5f  =z  +  39".2i:3".4;   St'  — -{-22". 

drouji,  1676-83. —  Here,  althoii<>'h  IIevelus's  (dock-error  seemed  l)etter  deter- 
niiiK'd  than  liefore,  the  observations  exhibit  anomalies  which  cannot  be  attributed  to 
the  apparent  accidental  errors  ol' observation,  and  which,  therefore,  leave  one  in  (h>ubt 
how  the  results  should  be  treated.  .\s  the  results  cannot  be  worth  a  refined  discussion, 
1  shall  simply  state  how  I  hav(^  used  the  e(piations.  The  emersions  of  Mars  and  of  a 
Tauri  have  been  retained,  while,  as  Ixd'ore,  all  other  emei'sions  are  rejected.  The  re- 
sults from  ,v  Orionis,  1678,  .March  28,  (Xo.  62),  and  fn.m  the  three  .stars  occulted  1683, 
April  2,  (Xos.  75-77),  have  been  rejected  on  account  of  discordance  of  residts.  In 
the  iirst  case,  the  identity  of  the  stai  is  still  in  doul)t,  while  in  the  second  there  was  an 
interval  of  nearly  two  hours  between  the  iirst  occultation  and  the  determination  of 
(dock-error,  du'-inn-  which  interval  the  error  had  to  ha  su)»posed  constant.  The  results 
of  the  occidtations  seem  to  indicate  a  large  (dock-rate.  Tliere  remain  nuie  equations, 
of  which  the  sum  has  been  taken  as  a  normal  for  determiinn;-'  di.    This  e(|Uiition  is: 


8.44  .5*  =  264"  ±40"; 


and  the  result  is 


EjKHdi,   1680.0:   (5i  r=  +  3i"±5";   iit' —-\- 16". 

'i'he  (dose  a,i>'reement  of  the  four  mean  results  derived  from  the  oljsorvations  of 
IIevemis  is  pundy  accidental;  the  disconhuice  of  the  individn.al  etpiations  in  yeueral 
indicates  that  the  [)robable  errors  we  have  assiniied  may  be  satedy  increased  bv  one 


third. 


Oh>icrv(if!i)iis  of  flic  Froich  (tstnDKimcr^t  idhI  of  Fi.amstked. 

A  preliminary  examination  of  these  ol)servations  indicated  that  tliere  was  no  sys- 
tematic difference  lietweeii  the  results  of  the  oecultiitious  ob.served  bv  Klamstkeu  aiid 
those  (d)ser\ed  by  the  French  astronomers.  They  have  thendbre  been  combined,  and 
.solved  so  as  to  obtain  corrections  to  the  moon's  mean  longitude  and  to  the  longitude 
of  the  node.     In  effecting  these  s(diitions,  we  meet  with  the  difficulty  that  the  correc- 


ftfiSEARCHES  ON  THE  MOTION  OF  THE  MOON. 


233 


tlon  to  the  tabular  mean  lon<,ntn(le  cannot  he  re<ranlo(l  as  increasinj.^  unitonnly  lor  my 
considerable  le-  ''i  of  time.  On  the  other  hand,  when  wo  divide  the  observations  into 
groups,  the  duration  of  each  group  is  too  small  to  permit  an  accurate  determination  ot 
the  corre-'"  -u  of  mean  motion  from  that  group  alone.  The  following  course  appeared 
best  ad'  .  .  for  the  present  preliminary  s.dutioii.  Hough  solutions  were  hrst  made 
so  as  to  give  the  value  of  '5^  alone  for  the  mean  epochs  of  the  great  groups  into  which 
the  observations  were  divided.     Thus  was  found : — 

For  1680,     de  —  +  30". 4,  Fi.amsteed's  observations. 

For  1682,     <5e  :=  4- 28". 5,  Paris  observations. 

For  1 710,     <?£  =  + 1 5".4,  Paris  observations. 

For  1715,     (Je— +  13". 8,  Delisle's  observations. 

For  1728.5,  Sez=:+    7". 3,  Paris  and  Delislk'.s  observations. 

From  these  values  of  the.  correction  of  mean  longitude,  it  was  concluded  that 
the  corrections  to  the  tabular  mean  motion  might  be  assumed  to  have  the  toUowmg 
values: — 

From  1672  to  1690,  Sn  =  — o".35. 

From  1699  to  1720,  f5»,  =  —  o".55- 

With  these  assumed  annual  changes,  each  residual  of  an  ecpiation  was  reduced  to 
a  mean  epoch  of  its  group,  all  the  observations  to  i  720  being  divided  into  two  groups. 
The  adopted  mean  epoch  for  the  first  period,  1672  to  1690,  was  1680.0;  that  tor  the 
second,  1699-1720,  was  171 2.5.  In  other  words,  the  abs.dute  term  of  each  e.piation 
was  corrected  by  the  quantity  o".35  /•  ( 1 680.0 -0  for  tlu,  iirst  group,  and  by  the 
quantity  o."55  A"  (i  7 1 2.5  -  0  for  the  second,  /,•  being  the  coetlicient  ot  Se  m  the  ecpnition. 

In  the  solution,  the  unknown  quantities  retained  were  f5f,  iSO,  and  '5/^0,  the  last 
being  an  assumed  constant  correction  to  the  nioon's  latitu.le.  TUU  was  kept  in  the 
equations,  because  a  constant  error  in  the  declinations,  and  therefore  in  the  latitudes  ot 
the  stars,  is  to  be  e.xpected,  and  will  show  itself  in  the  e(piations  as  a  constant  apparent 
correction  to  the  moon's  latitude. 

The  weights  assigned  to  the  several  equations  are  shown  in  tlie  last,  column.  1  lie 
probable  ernu-  depends  mainly  upon  the  errors  of  theory  and  of  the  place  (.f  the  star, 
so  that  no  distinction  with  respect  to  weight  was  necessary  in  the  case  of  fair  observa- 
tions. As  a  general  rule,  emersions  were  rejected  unless  there  was  positive  reason  to 
believe  that  the  reappearance  of  the  star  had  actually  been  caught  at  tlu-  right  ni.)nient. 
The  solutions  with  the  assigned  weights  lead  to  the  following  results:— 

First  group,  Cassini,  Flamsteeu,  La  Hire,  1672-1690. 

Normal  Equation-'. 

18.423*5* +  2.613  a^O— 1. 521  (5/^,-538". 27=0 

2.613      +4-750         —3-940       -    66^84=0 

-1. 52 1      -3-940        +7-059        +    25".59=:o. 


30- 


-75  Ar. 


234  Ri;si;.\Kciii:s  on  the  jiotkxv  of  the  moon. 

Solution. 

'5f    =  +  29".4i,  cpdcli  16S0.0. 

i,UJ  =  -{-    o".26. 

'W>„  =  +    2".,S6,  wv]}rhi  =  3.S. 

.Sucinid  yiMiii),  ( 'vssiM,  La  |[ii{i;,  1)i:i,i.si,k,  1699-1720. 

XiiniKil  I'jiiififidiis. 

31. 65  Sf  —  2,32  I  i'^0  +    0.753  '^''n  —  466".S4  =  o 

-2-321       +5-970         +    4.CS76         +     25"..S4:=o 

^■753      +4-<'^76         +i7-^>3  —     29".3ir:o. 

Solul'imi. 

'5^    r=-f  14".7S,  cpDcli  1712.5. 

'V/„  zz  +    o".S2,  wcinlit  —  13.4. 

'I'lic  corrections  i<)0  luivc  a  very  siiifill  weiglit  iu  botli  equations.  Occultations 
do  not  artbnl  good  data  for  dctcnniiiinj>-  the  correction  to  the  moon's  node,  because,  to 
he  favorahh',  an  oltservation  nuist  l)e  not  too  far  from  the  node,  and  must  not  bo  nearly 
central.  A  <>lance  at  the  equations  will  show  that  the  coelHcient  of  ifiO  amounts  to 
0.5  in  less  than  lialf  the  efjuations.  Moreover,  owinj)'  to  an  accidental  lack  of  .sym- 
metry in  the  occultations  in  each  grou}),  tlie  value  of  t69  depends  very  largely  on  that 
oi'  <%„,  the  approximate  expres,sions  being: — 

From  the  fir,st  group,        i(5(9—        i".47  —  0.S5  f5?(„. 
From  the  second  grouj),  }60  z=.  —  2''.  19  -f-  0.85  (%„. 

The  actual  value  of  61)^  and  (''519  should  be  consi<lered  nearly  the  same  for  both 
group.^,  being  proljiibly  about  one-iiftli  larger  for  tlm  first  grouj)  than  for  the  second, 
since  we  may  su[)pose  tlieni  to  vanish  al)out  1850.  The  mo.st  probable  values  of  Sb„, 
on  this  h^-pothesis,  are: — 

For  the  first  group,  6h„  =  -f  i".5. 
For  the  .second,         f5?>„  —  4- i".2. 

Wlience  we  .shall  obtain  — 

From  the  first  group,        /''>^  =  +  o".2. 
I'Vom  tile  second  group,  iSOzz —  i".2. 

To  obtain  a  really  definitive  result,  we  nmst  cond)inc  both  groups,  suppo.sing  the 
values  of  (h  ind(>pendent,  and  putting — 

iSO.,  —  0.80  ;<')0„ 
Shn    =0.80(5/;,, 

the  subscript  numerals  distinguishing  tlie  values   wliicli  pertain   to  the  two  group.s. 
The  coeflicient  0.80  presupposes  that  the  position  of  the  node  and  the  tabular  latitudes 


—  1-52 

—  0.04 
-|-  21.16 


53S".27  =  o 
—    4i".oo  — o 


o".7^  =  o. 


RESEAKClir.S   ON   Till:  MOTION   Ol'    TIIK  MOON.  2;,5 

of  t\w  stars  iuv  com^ct  nt  tl.o  cpccl.  1842,  wind,  is  iilnrnt  i.s  - 1  „  hypctlu'sis  as  we 

(•nil  nmkc.  'IMic  (•(n.ilmii.ti.ni  ..f  tlit^  two  j.'n.ui.s  lias  Ik-ou  made  on  llic  supposition 
that  all  tliooqimtionsofthosocou.l  -n.np  arc  (irsl  innltiplicl  l.y  ..25.  and  tliat  ;''iO.,an.l 
dh,:uv,  tluM.  ivplar,(Mll)V0.8o^A-9,  an.l  0.80  .W>,  This  conrs.-  is  tak.-n  hccans..  th(, 
residuals  show  that  tlu^  unit  of  woij-ht  coiTcsponds  to  ii  smaller  pn.l.ahlc  error  ni  the 
suc-ond  i^Toiip  than  in  the  tirst.     The  conihint'd  normals  arc:— 

39.56  <U.,  +    0.00  <U,  —  2.32  /'<0,  +    0.75  'Wy,  —  5i^3"-55  =  o 
0.00        +IS.43       +2.61 
—  2.32        +    --61        +953 
0.75        —    1.32       —0.04 

The  s(dntiou  of  these  e(inations  ;;ives — 

fif.^    —4- 29". 38  i:  I ".o:  ei)och,   1680.O. 

•5*.,    =+ I4".78  ±o".6:  ei-och,  i  7  1  2  5. 

i('irJi=.~    o".i4±i".2;  wei-j,-ht=    9. 

fW>,    =:+     i".76  ±o".S;  wei-ht  =  2i. 

The  prohiible  error  of  each  eipiatioii  of  wci-ht  unity  is  about  3".6;  and  as  all  the 
o.piations  of  the  second  series  were  multiplied  by  tlw  factor  1,25,  the  prol.ahle  error 
of  each  observed  distance  of  centre  (.f  moon  from  star  would  be  alx.ut  3".o,  which  is 
the  error  already  estimated  from  ern.rs  of  star-places  and  of  the  tabular  p.M-turbations 
and  from  the  irrejrularities  of  the  moim's  limb  It  i.s,  therefore,  from  these  sources, 
rather  than  from  errors  of  the  ..bserved  times,  that  the  errors  of  the  ...piations  arise,  so 
that,  when,  in  the  course  of  time,  the  tal)ular  perturbations  and  the  places  of  the  stars 
are  more  accurately  d.^tenniued,  more  accurate  results  may  be  obtained  troni  these 
occultations. 
Obscrrations  of  CxsHis\  at  Paris  nml  \)v.\axia:  at  St.  I'rtrr.shtirf/,  hrhrm,  ly 20  anil   1750. 

i  have  not  attempted  any  serious  discussion  of  these  observation^  having-  merely 
sou<.-ht  to  obtain  from  them  an  approximate  correction  t..  the  mean  lon-itU(U>  tbr  some 
epoch  near  1725.     From  the  good  observations  between  1725  and  1730  inclusive,  we 

ttnd:— 

Kpoch,  1728.5:  (>)*—+ 7".3  (8  observations), 

a  result  I  look  upon  with  a  snspicioii  of  its  beiii-  a  little  too  large,  owing  to 
several  of  the  observatums  on  whicdi  it  depends  having  been  made  at  the  moon's 
bright  linilj. 


23^> 


Ri;si;.\U(;iiKs  ON  tmk  motion  of  tiii:  moon. 


§  14. 
OI5SI':i!VATI()NS  OK  KCLIPHKS  FROM  ir.jo  TO  1724. 
Tlu!  tiihiiliir  pliu'cs  of  tlio  sun  which  aro  used  in  the  ruchictioii  of  tlioso  uclipsos 
were  iicc,i(hMitiilly  oinittod  in  §  11,  wIkm'u  tlio  corro.spondinir  places  of  the  moon  aro 
{ifiven.  Tlicy  aro,  tlicrcforc,  };iven  in  the  following  tabh'.  Thoy  wore  j^onorally  coni- 
piitod  for  dirt'oront  moan  timos  l>y  dilforont  coinpiiter.s,  in  order  that  the  conipariHon  of 
the  resnUs  nii<,dit  serve  as  a  cheek  on  the  accuracy  of  the  work.  Tho  ori^nnal  results 
are  all  presented. 

Lon>;ilin/i-s  of  the  Sun,  from  Hanskn's   Tables. 


D.itc. 

Greenwich 
Mean  Time. 

Longitude 
Mean  Etjuinox. 

1 

Date, 

1 

Greenwich 
Mean  Time. 

l.ongilude 
Mean  E<|uinox 

1, 

III 

s 

" 

h 

III         s 

. 

. 

., 

l62[.  May  20 

12 

0 

0 

59 

54 

17.2 

i()S4,  July 

12 

0 

0       0 

no 

46 

12.2 

"          *' 

18 

39 

34 

6d 

10 

I7.5 

"           " 

2 

Id        0 

no 

51 

36.8 

" 

21 

5 

In 

f)() 

Id 

f..7 

12 

0        0 

III 

14 

49-5 

"                      " 

24 

0 

0 

Ck) 

23 

7.0 

16S7,  May 

II 

0 

0       0 

50 

48 

33-9 

1O33,  .\|,i,     8 

-  'J 

21 

IS 

49 

44-4 

" 

I 

0        0 

50 

50 

58.0 

"                      '* 

■» 

4S 

1) 

!'J 

I 

53-7 

"           " 

12 

0        0 

51 

'7 

27-5 

1639.  Jl'"^         » 

0 

0 

0 

70 

34 

56.8 

1689,  Soi)l 

'3 

0 

0       0 

171 

14 

54-4 

"                      '* 

3 

3f' 

0 

70 

43 

33-2 

"           " 

3 

20        0 

'-I 

23 

3-5 

*'                      " 

12 

0 

0 

7' 

3 

33.7 

"           " 

12 

0        0 

■71 

44 

12.9 

1645,  Aug.  21 

0 

fj 

0 

143 

34 

I9-5 

1699,  Sept 

22 

12 

0        0 

180 

8 

18.3 

1652,  .\pr.     8 

0 

't 

0 

19 

'3 

46.4 

"           " 

21 

0        0 

180 

37 

45-2 

:f)5i,  Aug.  u 

12 

0 

0 

'39 

14 

52.0 

1706,  May 

II 

12 

0        0 

50 

42 

54-2 

.. 

20 

0 

0 

'39 

34 

4-9 

" 

20 

20        u 

5' 

2 

59-1 

.. 

24 

0 

0 

139 

43 

42.3 

24 

0        0 

51 

II 

4S.5 

165(1,  Jan.    2O 

0 

0 

0 

306 

20 

48. 4 

1703,  Sept. 

«3 

12 

0        0 

171 

9 

S.o 

,. 

0 

30 

0 

306 

22 

4.6 

" 

18 

30       0 

171 

25 

5-2 

" 

12 

0 

0 

30f) 

51 

15. s 

24 

0        0 

171 

33 

30.5 

1675,  June  22 

II 

0 

0 

91 

33 

18.9 

;  1715,  May 

2 

12 
19 

0        0 
12        0 

41 
42 

51 
8 

20.2 
45-5 

l6f)i,  Mar.  29 

12 
21 

0 
0 

0 

0 

9 
10 

43 

5 

36.3 
48.0 

" 

• 

24 

0        0 

42 

20 

22.2 

1724,  .May 

22 

0 

0        0 

61 

2O 

25.8 

1&6O,  July     I 

12 

0 

0 

100 

8 

14.7 

12 

0        1) 

Oi 

55 

13-2 

" 

17 

36 

0 

I(K) 

21 

35-2 

"          " 

24 

0        0 

62 

24 

0.0 

" 

24 

0 

0 

100 

sft 

50.3 

1676,  June  10 

12 
20 

0 
0 

0 
0 

So 
3o 

40 
59 

27. S 
33.3 

. 

24 

0 

0 

81 

9 

6.0 

The  observations  in  question  may  be  divided  into  two  cla.sses:  observations  of 
contacts  and  of  ])hases.  The  latter  wore  freuerally  estimated  l)y  throwinjif  the  sun's 
imajio  upon  a  screen  so  adjusted  that  the  outline  of  the  image  should  coincide  with  a 
circle  drawn  on  the  screen.  The  radius  of  this  circle  was  divided  into  12,  30,  or  32 
parts  by  concentric  circles,  so  that  the  correspond! nj^  phases  of  the  eclipse  could  be 
observed.     The  absolute  maj^nitude  of  a  phase  thus  determined  is  necessarily  too 


RESEARCIIKS  ON  Till;  MOTION  OK  Till;  MooN 


-.■>/ 


iiiicertiiiii  to  ho  rulii'd  uii,  iiwiii;;'  to  the  nH'cct  ot'  irriulliitioii  ami  distortion  of  imiij;(^; 
hut,  so  far  ns  loiifj^itudo  is  coiiconu'd,  this  oll'oct  will  act  in  opposite  dircctiinis  hct'ore 
and  aftor  the  tliuo  of  j;reatest  eclipso.  'riierefore,  hy  snl)tiactitij^'  from  each  other  tlio 
correspondiiiff  ol)servatioiis  hoforc^  and  after  the  middle,  we  slinll  olitain  results  nearly 
frco  from  tlu;  errors  in  (|iU'stion.  This  is  the  course  which  has  hccMi  ;^enerally  adopted 
in  tho  discussion  of  these  olworvatioiis.  \VheU(!ver  possihlc,  ohservations  at  nearly 
0(pial  distances  (m  oadi  side  of  tho  niiddlo  have  alone  heeii  compared,  the  mean  of  two 
or  more  liein<;  somotiuies  comhined  with  a  sin;;'le  corrcspondin;^'  one  on  tin-  opposite  side. 
When  the  ohservations  were  so  lu'oken  that  there  was  no  correspondence,  the  comhi- 
uation  wiis  made  in  the  way  which  seemed  adapted   to  "^ive  tlu;  most  prolmhlo  result. 

The  details  of  reduction  are  presented  pretty  fully  in  the  following;'  forms; — I'nder 
the  head  of  each  eclipse  is  ijiven  the  apparent  semi-diameter  of  the  the  moon  as  seen 
from  the  station  at  th»f  l)e;;Mnnini;'  and  at  the  end  of  the  eclipse,  com|iuted  with  the 
same  data  and  in  the;  same  way  as  in  the  ease  of  occultatioiis.  The  sun's  a])parent 
semi-diameter  is  c(unputed  hy  supposin;^'  its  value  at  distance  unity  to  l)e  960".  [n 
souuf  cases,  however,  it  may  not  exactly  corres])ond  to  this  constant,  some  \alue  a 
little  ditfereiit  heinj-'  used.  Any  small  error  in  the  semi-diamet<-r  Ikmui^-  in  i^reat  part 
eliminated  fnmi  the  result,  no  fireat  pains  wen  taken  with  it. 

The  local  mean  times  of  the  ohserved  phases  are,  for  the  most  ])art,  derived  from 
data  already  f,nven  hy  applyinji-  the  clock-corrections  deriv(^d  from  altitudes  or  other 
sources.  In  the  oliservations  of  (Ja.ssknius,  the  times  are  derived  immediately  from 
the  observed  altitudes. 

This  tinu)  heiui;-  nsduced  to  Grecmwich  nu^au  tinu',  the  apparent  position  of  the 
moon  as  seen  from  the  station  is  computed  in  the  .same  way  as  for  the  occultatioiis, 
except  that,  instead  of  usiiij^-  the  parallax  of  tiu;  moon,  only  the  difference  of  parallaxes 
of  the  sun  and  moon  ;ire  emph)yed.  I'Voiii  this  reduced  pt)sitioii  of  the  moon,  and 
fnmi  the  f^^eocentric  position  of  the  sun,  an;  derived  the  tabular  distance  of  the  <'eiitres, 
which  is  (•■iveii  in  the  c(dumii  followinji'  the  mean  times.  To  this  taljular  di.stance  is 
added  its  ditfereiitial  c<ietHcieiit  with  respect  to  th(i  moon's  mean  loniiitiide. 

This  is  followed  by  the  observed  distance  of  centres  as  derived  from  the  contacts 
or  measures  of  phase  made  by  the  observers,  the  formula'  i)ein<|^:— 

I)  —  s  +  s'  —  III, 
III  being'  the  maj^iiitude  of  the  eclipse,  which  was  usually  expressed  in  terms  of  the 
sun's  .semi-diameter,  and  .s  and  s'  the  a[iparent  .semi-diameters  of  the  suu  and  moon 
respectively.     If  A  exjjressed  the  nund)er  of  dij^its  eclipsed,  we  should  have: — 

As 
'"=   6  • 

In  the  case  of  contacts,  in  would  represent  the  magnitude  of  the  least  noticeable 
eclipse  at  be<>'inuinj^',  or  the  magnitude  innuediately  less  than  the  hjast  visible  at 
ending.  These  two  values  of  111  are  rejin^sontod  l)y  «,  and  a..,  and  in  combining 
observations  of  contacts  we  have  always  supposed — 


At  the  same  time,  double  weight  is  always  given  to  an  observation  of  ending,  as  com- 
pared with  that  of  beginning,  because  the  oljserver  is  less  likely  to  fail  in  noting  the 


lUCSKARCIIES  ON  Till.  MOTION  OF  TIIK  MooN. 


time  wlicii  tlu^  ('(tlipsc  (lisM|i|(c;ii's  tliini  wlifu  it  ii|iit(':irs.  \\\  tliis  (■((iiildiiiitinii,  flic  nicjiii 
rcKiilt  t'nmi  tlio  l»(',n'iiiiiiii;i'  find  ciid  ot'  iiii  (u'li|»-ii'  is  iii(l('|)('ii(li'iit  ut'  die  vuliic  wliirli 
iiiny  Iti'  iissio'iit'il  to  (C,,  iiml  flicrct'nn'  due-*  nut  i'c(|iiii-c  iiiiy  iiivcstiji'fitioii  ii|'  flic  viiliK* 
ot  lliiit  (jiiiiiitity.  Wi-  iiiiiy  sim|)i\-  rc;;;inl  a,  and  a^  as  zero,  iiiid  ;^ivc  doiildc  wi-i^-'lit 
tu  tlic  oitscrviitioii  of  tilt'  Olid  ul'  tluj  f(di|)sc  ms  c.oiniiiinMl  with  tlint  of  hcifiiiiiiii;;'. 

Ill  coiiihiiiiiiji' ohscrviifioiiH  of  coiitfift"*  and   phases  to  (ditaiii  a  mean  result,  it  has 
lieeii  supposed  that  one  pair  of  eoiitacls  is  worth  three  or  four  pairs  of  ohser- 


lieiierallv  iieeii  sii 


vatioiis  of  phase,  tlii'  ]iroportioii  varyiiiji'  with  the  apparent  accnratn"  of  the  oliservi 
tioiis  of  phase.     In  a  I'vw  oases,  wcijilits  are  assigned  to  the  ol)s<;r\atioiis  of  phases;  Itiit, 
ill  f^-enernl,  there  arc  no  (hita  for  siudi  an  assi^iiinieiit. 

'To  facilitate  the  final  discussion,  the  dillereiicc  Ix-tweeii  (iacli  obsorved  and  tahiilar 

This  ditVereiice  is  the  ahsoliite  term 


ion. 


distance  is  ^'iveii  for  ea(di  separate  o]»ser\at 
of  an  ('((nation  c(nitaiiiin;;'  <h,  and  an  unknown  c(niil)ination  of  (|nantiti('s  dupeiid- 
tlie  mode  of  ohservation,  which  are  supposed  to  he  a  fitnction  of  />. 
This  combination  is  eliminattid   from  cacli  pair  of  (d)scr\atioiis,  at  e(|iial  distaJieos  on 


imi'  on  errors  ii 


each  side  of  the  middle, 


in 


tl 


le  manner  iilrea(l\-  descri 


bed, 


leaviii;^'  an  e(piatioii  in  e 


aloiio.  It  has  not  been  c(jnsidered  necessary  to  write  down  the  individual  e(|iiations 
thus  formed.  The  most  probable  rfjsnlts,  (••eiierally  (dttained  bv  citmbiniii^'  tlie  etpia- 
tioiis  ill  a  suinmary  maniier,  appro.ximately,  thoiifili  not  strictly  by  the  iii('tho(l  of  leaj^t 
s(iiiares,  are  "i'iveii  in  connection  with  each  set  of  obs(!r\  atioiis. 


Eclipse  of  1621,  .1/^f/y/  20,  ohsrrrcil  hi/  (}  asskndis  ((t  Air. 

|)parciit  semi-diameter  at  bej^'iimiiiji' q36".4 

Moon's  apparent  M-nii-diamettir  at  end 942". 7 

Sun's  apparent  semi-diameter 949". o 


M 


0011 


Local  .M.  T.,  19''    I'"  S7"-  Tabular  distance   if  centre; 


19S0  .7  —  1.00  '5* 


Observed  distan(r(M>f  centres    .    i,SS5".4  —  n, 
21''  27"'  I  7^  Tabular  distance  of  centres      .    i<S2  7".4 -j- 0.9.") '5f 
Observed  distance  of  centres    .    iiS9i".7  —  a.,. 
liesult  from  iirst  contact <5f  ^^ -(- 95" -f- «i 


l\os 


ult  f 


roiii  last  contact 


f5f  — -f  69' 


Mean  bv  woijihts 


<h 


:+7S' 


The  values  of  a  come  out  negative,   a   result   which  can  l)e  attributed  only  to 
errors  in  the  determiuatious  of  time. 

Erliihse  (if  1630,  .Ihhc  10,  nhscrvcd  hi/  (Ja.ssk.xous  (tf  I'aris. 

Moon's  apparent  semi-diameter  at  beginning 946". 2 

Sun's  ap])areiit  seiiii-diametcr  at  beginning 946".© 

At  6''  15'"  i».  Tabuhir  distanco  of  centres I9i2".8 

Observed  distance  of  centres ]<S92".2  — a-, 

Tfesult  of  the  observation  of  first  contact        ...       '5^  —  -f-  20"  -f-  a^ 
The  value  of  «,  may  I)t3  conjocturally  estimated  at    15",  giving  as  the  result 

'5£  =  +  35". 


RKsr.AUciir.s  on  nii'.  NutiioN  or  tiik  moon, 


UV 


/',(7//.ic  ii/  1633.  .l/'ri/  S,  oi'.t 


1/  I'V    (IasSKMH.'s    i//    /)iiill<\        (SfU  |).  Hi.) 


Moon's  jpiKiicm  scinl-iliaii'ci 


.It  I 


I'KiniiiiiH; 


Moon's  apiiarunl  suiiii-dlamrlcr  M  cnil 


Sun'- 


s  irnii-ili.iiii'ii'r , 


IJ33".1J 
'>57  •» 


Ohs.  All.     I.'x.il  Mr 


T.ihul.ii  DiM.ol       Oil' 


III©. 


15  : 


21  33 

20  .|8 

•J.I  2( 

Icj  30 


18     16 
16     M 


15 


'5     3'J 
1;     23 


14     ?7 
I  I     22 


13 


44 
34 


II  3S 

II  ic) 

I"  I? 

c)  52 

')  5 


lillK' 


3     57 


4  27-5 

4  3'>-3 

4  34. 'I 

4  Jf'.'j 

4  42-" 

4  44-fi 

4  41)-/ 

4  5fi.') 


I.fi 
5-1 


10. S 


V 


22.3 
1 7. 1) 


II. s 


IJ.4 


-0.8IJII 

-0.83 

-0.58 


-0.36 

-o.2fi 
—0.04 


4     +o.o3 


12.7     +0.(18 


13- 

13- 


14.5 


+  0.71 
+  11.74 


15-7      +'J- 


5  14.1  I7."  +i>.'^4 

s  17.2  i>.2  +0.S6 

5  20.0  Ii>.4  +0.8S 

5  20. ij  II). 7  +0.88 

5  23.0  20.6  +0.S1) 

5  2(i.  I  22.0  +0.()0 

5  27.1)  22.7  +O.I)I 

5  31.11  J4.I  +o.i)2 

5  36.0  2fi.3  +11.1)3 

5  40.4  2S.4  +o.()5 

5  4ri.i  31.07  +11.1)7 


Disia 


II).. I : 
If)  J. 

la.o 
II. f. 


'^•5 


II.Ci 
12.4 


13-4 


I5-" 
ifi.i) 

17.4 

lS.2 
II). f) 


Tnliiila 
Disi. 


2.7. 
1-5 


+    11 

+  0.5 


+   0.1 


+   0.2 


-   '1.4 


+   0.3 
+   0.5 


+   0.4 


+  "-4 


\Vl. 


23-5  H-    'o 

24.3  I  +    I.fi 

2f).2     2;.S  +   I-') 

27.2     27.3   I  +   I." 

21).  I      21). fl    j  +1.1 

31  .;o  —  "J  I  +  ".4 


I    t 


Wlun-e  two  obsorved  <listanc(;s  are  given,  the  second  is  from  the  ih-'rees  of  tlie 
ciremnference  eelipseil  A  tvpoo-niphiciil  error  in  the  printed  record  of  the  hrst  ohser- 
vation  renders  the  time  doni)tfnl.  The  eorri;spondence  of  tlie  second  oliservation  to 
the  time  jfiven  is  entirelv  eonjectnral.  'Die  nine  or  ten  foUowing  ones  are  ot  very 
little  wei-^it  for  determininj.'  the  moim's  longitnde;  l)nt  the  minnteiiess  of  the  correc- 
tion whirii  thev  indicate  to  the  tabnlar  distance  of  centres,  at  the  time  of  greatest 
eclipse,  seems  'to  show  that  ({as.skni.i'.s's  determinations  of  the  magnitude  ot  the 
eclipse  were  nearly  free  from  constant  error.  1  have  therefore  nsed  all  the  subse- 
,pient  measures  with  the  weights  as  given,  and  the  resulting  correction  to  the  moon's 


mean  longitude  is 


(!)f  =  +  o'.cSS  -+-:,l". 


240 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Eclipse  of  xdyy,  yiiiic  i,  obsenrd ly  Vj,\f,co\i:tiv.  11/  Mii/i/lchmin. 
<'  =  53"45';  /^f)"'  8«W. 

(St'l-  Fl.AMSll'.Kl),  llisloy'hl  Cih-li-slis,  vol.  i,  p.  2.) 

Moo:i'>' -.pp;irenl  senii-diametui  at  beijinning    .      .      .     gsi/'.o 

Moon's  a|... arum  si.'mi-diamfti;r  ai  cTid <)35' -4 

Sun's  apian^nt  scmi-diainctLT 945".*) 


No.  of 

Obs.  Alt. 

Local  Mean 

Tabular  Dist.  of 

Obscr\ 

j  Phase. 

of©. 

Tinii'. 

Centics. 

Dislan 

I 

3f>  35 

/;  m     s 
3  48  04 

I(j3f)  -  ,95,\t 

18S5  - 

2 

33  51 

4  f)  58 

1449  -  .9: 

1450 

3 

3"  47 

27  47 

912  -  .87 

881 

4 

26  3r 

5f'  49 

343  +  .02 

360 

5 

25  58 

5  0  27 

348  +  .3' 

369 

6 

25  20 

4  45 

390  +  -59 

483 

7 

23  23 

iS  0 

668  +  .91 

748 

S 

21  38 

29  58 

987  +  -97 

1059 

9 

20  53 

35   7 

1132  -1-  .98 

1220 

10 

20  U 

39  S<> 

1270  -1-  .98 

1315 

II 

19  28 

44  54 

1415  +  -99 

1(46 

12 

iS  12 

53  42 

1676  -h  .99 

1700 

13 

17  2U 

59  47 

185S  +  .99 

iSSi  - 

Cor 

r.  to 

Tal 

ular 

n 

is'. 

51 

H- 

1 

- 

31 

+ 

'7 

+ 

21 

+ 

93 

+ 

80 

+ 

72 

+ 

88 

+ 

45 

+ 

31 

■+■ 

2J 

" 

23 

The  contacts  iilono  here  givo, 

<5f -  + 33",  wt.  =  8. 

Phuse  2,  coiuparcd  witli  tlio  lueaii  of  10,  i  [,  and  12,  <^'ivo.s  the  equation  1.92  Se=. 
+  32",  wlience 

<ie  =  -f  1 7",  wt.  =  4. 
Phase  3,  crMn[)aretl  M'itli  the  mean  of  7  and  8,  gives  1.81  dtrz  106",  whence 

'5f=:  +  59",  wt.  =  3. 
Giving  the.so  results  the  respective  weiglits  u-ssigriod,  we  have,  as  the  ni'^an  ••nsult, 

'5f=  +  34"  ±  10". 


RESEARCUKS  ON  TIIK  MOTION  OF  THE  MOON. 

luiipsi  !>/  iCf^f).  yuni-  i ,  obscn'cl  by  \\itv.v.o\.  al  or  iinu-  7ik\I,//i  l\iih. 

0  =  53    20  ;    .1  —  II'"  4S'.4  W.  from  C.iui-nwicli. 

Moon's  apparent  senii-diameler  at  begiiinini;      .      .     03')  ■' 

.      .      •      03?"-" 
.      .      .      9-15".^' 


241 


Moon's  apparent  semi-diameter  at  end 
Sun's  apparent  semi-diameter    . 


Corr,  t(j 


^ocal  Mean 

Taliular  Disl.  of 

Observed  .. 

ainilar 

Wt. 

Time. 

Centres. 

Distance. 

Dist.  1 

h      m      s 

i 

" 

" 

3  43  '8  ■ 

l()ii  -  .04'''' 

1886  —  "1 

-  25 

47   3 

1817  -  .04 

1809*      ! 

-  8  i 

1 

2 

50  48  , 

1722  -  .04 

if'O"     i 

-  25 

• 

53  33 

1652  -  .03 

if)2q       ; 

-  23 

2 

59   3 

1511  -  -03 

1 507 

-   4 

4   3  48 

130"  —  -02 

I38I      1 

-  9 

8  48 

1262  —  .0' 

1255    i 

-  7 

10   3 

1231  -  0" 

1223       ; 

-   8 

• 

12  18 

1174  -  •''0 

1 1 60 

-  14 

17  33 

1041  —  .87 

1002 

-  39  ' 

20  iS 

.)72  -  .86 

941 

-  3' 

2 

■It      3 

827  -  .81 

813 

-  ^^ 

32   3 

f)S',  -  .75 

&55 

-  34  i 

35  48 

603  -  .70 

591 

—  12 

2 

43  33 

455  -  -46 

454 

—  I 

2 

48   3 

307  -  -2' 

461 

-i-  4 

2 

50  iS 

381  -  .05 

38;     ' 

+     4 

57  18 

307  +  .44 

417 

-h  20 

5   6  18 

530  +  -VO 

559 

+   20 

2 

9  33 

610  +    .84 

1   622 

+    12 

t. 

«4   3 

714  +  -89 

732 

4-  18 

2 

21  33 

'   910  4  .05 

037 

-t-  27 

2 

24   3 

()76  +    .ip 

I  OCX) 

+  24 

35  18 

I2q2  +    .98 

I33f, 

+  44 

38  33 

1385  +  -98 

1441 

+  56 

41  33 

'     1472  +  -90 

1504 

+   32 

43  48 

1537  +  -00 

1578 

+  4> 

a 

4f'   3 

if)03  T-  .90 

1630 

+  27 

• 

48  18 

1  1670  +   .99 

1693 

+  23 

40   3 

1692  -*-  .09 

;  1725 

+  33 

54  33 

184^1  +  .99''' 

1  1883  —  nj 

+  37 

•Derived  from  "  rircnmferi'iilia  r.iiip'-al.i"  33 


The  original  observations  are  found  in  IIoRK'.ix's  Ofiiis- 

aih  Astiviiomici,  London.  lf)73.  l>;l,^l■  327.  and  asnin  on 

I  page  3S8.     I  '--ould  not  learn  the  exact  position  of  I1"U- 

Rox:  the  longitude  given  aliove  and  employed   is  taken 

from  a  map,  but  the  latitude  is  that  given  by  Hokrdx. 

The  separate   results  for  reducing  the  clock   to  mean 

i  iiuk  as  derived  from  altitudes  are:  — 


Cloi 

k  T 

me. 

/( 

m 

,f 

2 

30 

I) 

2 

38 

0 

3 

IS 

45 

4 

'5 

15 

5 

■7 

45 

5 

59 

30 

fi 

5 

45 

(> 

/ 

15 

b 

8 

45 

f. 

lO 

30 

(1 

12 

45 

fi 

17 

15 

Correction. 

}it 

—   2 

2fi 

-  2 

37 

2 

37 

—  0 

5') 

—  1 

5S 

—  I 

3 

—  2 

f> 

-  3 

I 

-  2 

4f' 

—  2 

4f' 

—  2 

20 

-  ' 

55 

Mean 


-   2      1 2  ±  S« 


Tlie  (••mtacts  alone  ji'ivc (5£_4-34; 

The  obsorvatiou«  of  plias,. rS.  =  +  27     ( i  2  pairs); 

The  phase  from  aiijjU'  eclipsed  .     •     •     ■     •     '^t  —  -\-    ^'  ■ 
The  most  pmibable  mean  from  all  the  observations, 

r5f  =  +  27". 
.Tndo'ln-  fnm.  the  .liseordance  of  the  m.  asnres,  the  probable  error  .tf  this  resnlt 
wo,.ld  n,;  exceed  3";  Lnt  the  possibility  of  systen,>.ie  ern.r  ,nnst  ^ ^^.^.^.  .^^^^. 
We  can  hardlv  suppose  a  set  of  observations  n,a,V>  at  tins  epoeh  to  wne  a  p.ob.,1.1. 
error  less  than"  <':  ami  when  we  a.Ul  the  nn^-rtainties  respeetn.o'  eh.ck-em.r  ami  «eo- 
Kraphicul  position,  the  probable  error  may  be  in.'reased  to  S  or  9  • 
;n 75  A  p.  2 


24: 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Rdipse  (>f  1639,  yiiw  1.2,  (>/isit,vJ  i'v  C.assic.vdus  iil  Aix. 

'?  =  43    32'  ;   >=2i"'  47"  W. 

Moon's  apparent  semi-dianieler  at  beginning     .     935".o 
Moon's  apparent  senii-ilianieler  at  end      .      .      .      ()3o".() 


V4/      J 

1   '0 

<0 

1/) 

.2 

,   0 

1 

Local  Mean 

i       Time. 

1 

Tabular  Distance 
of  Cei.tres. 

Observed 
Distance. 

Corr.  to 

Tabular 

Dist. 

Obs.  Alt.  of 
0. 

c 

s  . 
3 

• 

Tabular  Distance 
of  Centres. 

Observed 
Distance. 

j 

^    Corr.  to 

1    Tal)ular 

Dist. 

1       ' 

//      m 
4  40.9 

31. 8  — o.S9'W 

i 
3"--l-"i 

-0.4-0, 

19  -15 

5  30.3 

12.  T  — 0.44 (if 

II. 8 

-"•3 

28  10 

'       A-i'i 

30.8  -    .88 

31.4-O] 

19  30 

31-7 

II. 7-   .40 

II. I 

-0.6 

28      0 

44.0 

30. 5  -    .SS 

29.8 

-0.7 

19  25 

32.2 

1 1 . 6  -     37 

10.8 

-0.8 

'  27  -10 

■(5-9 

29.6-    .88 

29.4 

—  0.2 

■9     5 

34.1 

1 1 . 1  —    .30 

10.3 

—0.0 

1  27  20 

47.8 

2S.8  -    .87 

28.3 

-0.5 

.855 

35-0 

10.9—    .26 

10.2 

-0.7 

1  27    0 

41)- 7 

28.0-    .87 

27.7 

-".3 

13  36 

36.8 

.0.7    .      . 

9.9 

-0.8 

1  26  37 

51.9 

27.1  -    .86 

27.1 

0.0 

18     0 

40.2 

10. r    .     . 

lo.o 

—0. 1 

,  26  to 

54.3 

26.0  —    .85 

-5-7 

-0-3 

17  16 

44-4 

10. 0    . 

9.9 

—0.1 

\  26     2 

55- 1 

25-7  -    -Ss 

25,0 

-0.7 

16  40 

47.8 

■.0.2    .     . 

9.S 

-0.4 

■  25  30 

58.0 

24.4-    .S4 

24-5 

+0.1 

16    0 

51.6 

10.7  +   .51           \ 

10.5 

—0.2 

!  25  24 

5S.6 

24.2-    .84 

23.7 

-0-5 

>5  30 

54-5 

II.3  +    .f>2              , 

II. 7 

+0.4 

;  25   " 

5     o.S 

23.2-    .83 

22. S 

-0.4 

15     0 

57-4 

I  2 . I  +    .68 

'2.7 

+0.6 

24  40 

2-7 

22.4  -    .83 

21. 9 

-0.5 

14  40 

59-4 

■2.7  +   .73 

13.0 

+0.3 

i   2)   25 

4.1 

21.8  -     .82 

20.9 

-0.9 

13  5S 

6     3.5 

■3-9  +    -78 

14.0 

+  0.1 

24     5 

fl.O 

21.  I  —     .80 

20.0 

-I.I 

13  35 

5-7 

14.9  1-     Sl 

14.9 

0.0 

23  40 

S-3 

20.1  —     .78 

19.4 

-0.7 

13  25 

6.7 

15.3  +    -82 

15.5 

+0.2 

23  .30 

9.2 

I';- 7-  .77 

19.0 

-0.7 

>3     5 

8.6 

16. 1  +    .84 

16.2 

+0.1 

23  20 

10. 1 

19-4  -    .76 

18.9 

-0.5 

12  48 

10.2 

16.7  +    ,85 

16. 8 

+  0.1 

23     u 

12.0 

IS. 6-    .73 

18.2         1 

-0.4 

II   18 

19. 1 

20.6  -f    .91 

21. 1 

+0.5 

22  55 

12.5 

18.4-    .73 

17.9 

-0-5        [ 

II     0 

20.9 

21.5  +    .9' 

21.5 

0.0 

22  30 

14. s 

■7-5-    .72 

16.7 

-0.8 

10  37 

23.1 

22.5   )-    .93 

22.5 

0.0 

22    15 

Ift.2 

16.9—    .70 

r6.5 

-0,4        ' 

10  27 

24.1 

23-"  +    -93 

22.8 

—0.2 

22      (1 

17. f> 

16.4  -    .68 

15.6 

-0.8              ; 

10  10 

25.8 

23. S+   .94 

23.4 

-0.4 

21       2 

23.0 

14.4  -    .60 

14.0 

-U.4 

10    0 

26.8 

24.3  +    -94 

24.1 

—0.2 

20    30 

2f).I 

13-4-    -55 

12.4 

—  I.o         1 

9  45 

28.3 

25.0  +    .95 

25.0 

0 . 0 

20   20 

27.0 

'3.1  -    .53 

II. 9      ! 

—  1.2 

9  3" 

29.7 

25-7  +    -95 

26.2 

+0.5 

20    3 

2S  b 

12.6  -    ,49 

„.8       1 

-0.8 

g    0 

32.8  , 

1 

27-3  +    -95 

27.6 

+0.3 

The  ('onstiuit  error  in  tlie  observjitioiis  of  phase  would  seem  to  l)e  vei-y  small.  1 
have,  therefore,  used  tlie  tirst  four  certain  observations  of  |)has(!  by  themselves,  and 
in  the  ease  of  the  remainder  have  combiiKid  olwcrvatious  after  tht*  middle  with  corre- 
sponding-ones  before.     The  result  is 


<5trz:+o'.3Sr=  + 


RESEARCHES  ON  THE  MOTION  OK  TlIK  M(J()N. 


M,'^ 


Jiciipsr  of  16,^9,   yi'tu-  I,  ohcnrd  l<y  Hkvi;i,uis. 

Moon's  semi-iliamctcr  at  hcginiiing  .  1J3O  ".5 
Moon's  scmi-diametcr  at  end  .  .  .  932' ..) 
Sun's  senii-(liamcti;r 047 '•" 


Local  Mean  Talailai  t)ist.of    OlistrvctI 


I 

'oiis.  Disi,    Con.  to 


I  '  I  :Obs.  Dist.  Cdir.  to 

Local  Mean  Talmlai  IJisl.ol  Obseivedj    ^„rr  f,,,  Talmlar 


Time. 

Centres. 

Distance.  ■ 

corr.  10 
Irrad. 

,     Dist. 

T 

inie. 

Ccnlres. 

Distance. 

Irrad. 

Disi. 

/;       m 
5      >7-S 



3i-i; 

—  I  .  00  ri  1 

3I-39-"' 

3i-4-"i 

+  o.3-«, 

(1 

in 
23-9 

2.9  4-o.99(^( 

6.7 

4.3 

+  1.4 

5     28.1 

2f).0 

—  I  .  OU 

2(1.3 

25.8 

—0.2        1 

6 

25-5 

3.6   +0.99 

7-1 

4-7 

+  1.1 

5     J3-2 

23-5 

—  I  .00 

24.8 

24.1 

+0.6      ; 

6 

26.9 

4.3  +0.99 

7-4 

5-> 

+  0.8 

5     38. (. 

20. S 

—  I  .  0(.i 

24.1 

23-4 

+2.6 

t 

=8.6 

5.1    +0.99 

7-7 

5-4 

•t-0.3 

5     42.2 

IS.., 

—  1. 00 

21.9 

21.0 

+2.1 

6 

30.1 

5.8   +1.00 

8.5 

f>.3 

+  0.5 

5     45-7 

17.2 

-O.IJ9 

20.0 

18.9 

-t  '-7 

6 

32.6 

7,2   + 1 . 00 

10.7 

8.7 

+  1-5 

5     48.2 

I5.1) 

-I'-'W 

19. 1 

17.9 

+  2.0 

6 

34.2 

8 .  (J   +  1 .  "O 

11 .2 

9-3 

+  1.3 

5     50-7 

14.  f. 

-o.yy 

1S.5 

17-3 

+  2-7 

6 

3f'-i 

9.0  +1.C0 

12. 1 

10.3 

+  1-3 

5     53-2 

13-4 

-o.gg 

17.7 

16.4 

+  3-" 

6 

38.2 

10.2   + I . 00 

13  0 

II. 3 

+  I.I 

5     55-2 

12.4 

—  0 .  yS 

15.6 

14.1 

+  1-7 

6 

40.1 

1 1 . 1    -•- 1  .(,0 

14.0 

12.4 

+  1-3 

5     57-'> 

1  I  .2 

-o.gS 

14.0 

12.3 

+  1.1 

fi 

41.9 

12.0  +1  00 

i5-f> 

14. 1 

+  2.1 

5     5i).f' 

10. 2 

—  0 .  yS 

13.4 

II. (> 

-+-1.4 

6 

44.2 

13.4  + 1 . 00 

17.2 

15-9 

+  2.5 

f.       1.7 

Q.I 

-o.yS 

13-1 

11.3 

+  2.2 

6 

45.9 

14.3   +1.00 

18.1 

16.9 

+  2.6 

6       4.1 

7.9 

-o.()7 

12.5 

10.6 

+  2.7 

6 

49-3 

16. 1    +1.00 

.9.0 

17.8 

+  1.7 

6       fi.o 

f...J 

-"•1)7 

12.(1 

10. 1 

;  4-3-2 

6 

5''- 7 

16.9   + 1 . 00 

19.7 

18.6 

+  1-7 

(•)       8.0 

5-y 

—  0 .  </i 

11.2 

9.2 

+  3-3 

0 

r  2  •  7 

[  iS.o  4- 1 .00 

20.8 

19.8 

+  1.8 

f)     10.7 

4-5 

-0.05 

9.3 

7-1 

+  2.6 

6 

=  41 

18.7   + I . 00 

21.4 

20,5 

+  1.8 

6     1 1 . 9 

3-<) 

—  0.y2 

S.o 

5-7 

+  I.S 

6 

55-9 

j    19.7    +I-0O 

22.2 

21.4 

+  1-7 

6     13.4 

3-> 

7-4 

5-" 

1  "**' 

f, 

57.8 

i  20.8  +1.U0 

22.5 

21.7 

+  0.9 

(.     17.1 

1.4 

4.9 

2.3 

i+o 

7 

0.9 

22.5    4  I. 00 

22.8 

22.0 

-0.5 

f)     IS.I 

1.2 

3.f> 

0.9 

f 

-0.3 

7 

•-•5 

23. fi    +1.00 

24.4 

23.- 

—  0.1 

U     10.3 

I.  I 

4.0 

1-3 

+  0.2 

7 

-■3 

24.9   4-i.'>o 

25-0 

24    1 

-  t)-5 

6     21.0 

1-5 

-l-u.(j7 

5.6 

3-1 

+  1.6 

/ 

' 

:~.1  +1.00 

26... 

25.5 

—  0.2 

6     22.8 

2.3 

+  0.09 

6.2 

3.& 

,...3 

7 

12. u 

^  a8.<.  +1.00 

i 

3...^ 

31.3 

(+   2.7) 

IIevelii's  i^'ives  a  immltor  of  (Irawiiiji's  of  jiliiises  of  this  eclipse,  sliuv  il;-  tliaf  his 
iiLstnuiiciit  was  altoffethtT  out  of  focus,  the  cusps  of  the  sun  Ix'iufj-  .so  rounded  near 
the  time  of  i^-reatest  phase  that  tht*  arc  of  sunli^'lit  was  of  nearly  ■  ,ual  breadth  throiifi'h- 
(lut  For  this  reason,  and  also  because  tiie  times  depend  entirely  on  some  kind  of  a 
sun-dial  which  may  not  iiave  been  in  the  meridian,  tliis  eclipse  was  in  the  first  place 
rejected  entirely.  (See  p.  SS  for  original  note  upon  it.)  Hut  I  afterward  concluded 
to  reduce  it,  if  only  to  see  what  kind  of  a  result  would  l)e  obtain.  om  the  worst  set 
of  observations  found  in  his  work. 

The  irradiation  seems,  from  the  excess  of  abmit  ;/  near  the  observations  of  ^^reat- 
est  phase,  to  have  been  about  one-tenth  the  sun's  semi-diameter.  In  the  column  of 
corrected  distances  from  observations,  the  observed  eclipse  is  increased  by  its  tenth 
part  to  allow  for  this.  Owin^r  to  the  uncerttiinty  of  the  law  of  error,  1  have  only 
combined  observations  of  nearly  etpuil  phase  on  each  side  of  the  middle  in  the  same 
way  as  with  the  eclipses  of  Gas.skmm  s.  The  ontacts  are  rejected  entirely,  as  there 
is  clearly  a  mistake  of  several  minutes  in  the  observation  of  the  end.     The  mean  of 


244 


RESEAUCIIKS  ON  THE  MOTION  OF  THE  MOON. 


tlie  lirst  scvciittH'U  abscvvutitms  of  pliaso  <i'ives  jiii  (excess  of  ob.sorvod  ilistaiicu  Ixiforo 
till)  iniddlo  of  tlio  ii('li{>.><e  of  2'.03.  Tho  incaii  of  the  last  twenty  givos  an  excoss  of 
I '.14.     Tlii.s  wonld  indicate  a  tabular  correction  of 


=  /    7 


a  result  to  wliic.li  scarcely  any  weight  c;ni  be  given,  owing  to  the  uncertainty  whether 
th((  adjustment  of  the  instrunient  really  remained  the  same  dunng  the  eclipse,  and 
whether  the  dial  was  really  free  from  error. 

Eclipse  of  1645,  .iiii^iist  2\,  (>/><(-r,'ci/  fiv  Hevkliu.-^. 

Moon's  semi-diaim-'tcr  at  beginiiini^  <J5'/  .4 

Moon's  scnii-diamettr  at  end  .     ()57".4 

Sun's  senii-diametcr     ...  .      .     1)51  ".2 


,ocal  Mean 
Time. 

Taluilai  Dist.of 
Centres. 

Observed 
Distance. 

Corr.   lo 

Talnilar 

Uist. 

Ivocal  Mean 
Time. 

Tabular  Oisl.  of 
'"i-ntres. 

Observed 
Distance. 

(^orr.    to 

Tabular 

Disl. 

-  .-.     __-_ 

- 

.  , 

,,    -_■ 

. — . .. 

//      m     .< 

" 

ft 

A     m 

" 

.■ 

23    2()    37 

r)42  -  0.1J31I1 

191 1  —"1 

—  31— ('1 

0    34    22 

720   —  0.22  ill 

7t)2  (?) 

(+  42) 

2y    52 

1 87 1   —  0.92 

1S31 

-  40 

44     12 

682    +    O.IO 

683 

■+     1 

3f)    22 

1732  —  o.yo 

1O72 

-  60 

4^     22 

691    4-    0.25 

722 

+  31 

4'J    52 

1634   —  o.Sy 

•5<J3 

-  41 

53    32 

717    +    iJ-42 

762 

+  45 

45    22 

1541    -  0.S7 

I5'4 

-  27 

57    37 

754   +  0.54 

801 

+  47 

48    22 

147S   -  o.Sf) 

1415 

-  03 

1      4    42 

844   +  0.67 

880 

+  30 

58     52 

12O5    —  0.32 

1237 

-  28 

8    52 

q03    +   0.74 

960 

+  57 

0       J     22 

1 1  f)o  —  0.76 

IIlS 

-  42 

II      22 

943    +   0.78 

')W 

+  5f> 

10    22 

1048   —  0.72 

1039 

-     9 

15      12 

1013   +  0.82 

1078 

+  (.5 

14    22 

qSl    —  aji(> 

1)60 

—    21 

18     22 

1006   +  o.Sf) 

1117 

+  51 

II)    22 

899   -  0.59 

S80 

-  ly 

22        2 

1152   +   0.89 

1 191 

+  39 

23     52 

S35   -  0-50 

S22 

-  13 

2f)     37 

1226   4    0.91 

1276 

¥   50 

24    52 

322   —  0.48 

Sot 

—  21 

34    22 

13S6  +  0.95 

1434 

+  48 

27     52 

7S4    -  0.41 

781 

-    3 

50     22 

1730   4-  0.98 

1790 

+  60 

29    52 

7(11    —  0.30 

7(>2 

+    I 

51      52 

177"   +  0.98 

1830 

+  Oo 

32   52 

733.-  0.27 

742 

55    52 

l^ifjl    +  o.gq 

igog— n.j 

+  4S-", 

A  system  of  twelve  equations  of  cniidition  is  formed  l)v  sul»tractiii"'  the  first 
twelve  residuals  from  the  last  tw(dve,  contact  results  excepted.  The  solution  of  these 
equations,  .slightly  greater  weight  being  given  to  tht»se  near  the  beginning  and  end  of 
the  eclipse,  gives 

'5*- =  +54". 
From  the  contacts  we  have: — 


Meginning 


End 


from  which,  supposing  «,  rr  2  a.,,  we  have  6t=^-\-  42".     J  t«ke,  as  the  most  probable 
result  from  this  eclipse, 

'>'*  =  +  5'"- 


RKSEARCIIES  ON  TlUi  MUTION  OF  TIIi:  MOON.  245 

Hrlipsa  of  1652,  April  7,  ohscrri'il  hi/  Gassexdi's  ot  l)i</nr. 

The  cud  of  this  eclipse  occiiuTod  within  a,  few  miimtes  of  noon,  and  it  is  not  likely 
tliat  an)'  reliance  can  l)e  placed  upon  the  times  deduced  from  altitudes  diu-inf,^  the  last 
hour  of  the  eclipse.  I  have,  therefore,  concluded  to  make  no  use  of  the  observations 
of  Gassk.ndus. 

/idi/'sc'  of  1652,  April  7-8,  obicncd  by  Hevi;i.ius. 

Moon's  .ipparunl  semi-tliametcr  at  liCRinning  .  i)<}7"'7 
Moon's  aiiparent  scmi-dianieler  at  tiid  .  .  .  i)()f)".8 
Sun's  scmi-diameler y57  •** 


Local  Mean 
Time, 


Tabular  Dist. 
(if  Centres. 


Observed  Dis-    Corr.toTab.    Local  Mean     Tabular  Dist. 
lance.  Distance.  Time.  of  Cenlres. 


Observed  Dis-     Corr.toTab.! 
lance.  Distance.     '; 


h 
23 


h    m 


5    27 

i(>  32  : 
18  30 

21  2 

22  52 

24  4" 
26    54 

25  54 
31  45 
35  lo 
37  32 
3S  54 
4f'  5 
48    31 

6    26 


lOtq— 1. 101' f 
1629— 1. 10 

1558-  1. 10 
I5i5-i.0() 
1470— I  .OIJ 
I4Ii)-I0i) 
I305-I.1KJ 
1315  —  1.08 
1245-1.07 

1  1  ()2  —  1  .  0(1 

1  104—1  .05 

1072—1.04 

qlo— 1.00 

857  —  0.1)8 

562-0.53 


1955- 
1O04 

I53(> 

I5if' 

1476 

1436 

138& 

1317 

1253 

057 

loi)7 

1037 

S.,I 

838 

578 


1 579 
1509 
1487 
1447 
1 406 

1356 
1288 


4-3f' 
-25 

—  22 
+  I 
+  & 
+  17 
+  21 
+  2 
+   3 

-  5 

-  7 
-35 
-19 
-19 
+  lfi 


+  36 
-50 

-4>J 

-28 

-23 
->3 
-  9 
-27 


9  9 

12  34 

14  15 

27  55 

30  17 

39  f' 
42  II 
51  -  0 

53  5 

54  40 

14  54 
16  58 

15  25 
21  3 


538-0.421!' 
528—0.24 
527-0.14 
652  +  0.51 
690  +  0.58 
864+0.76 
931+0.80 
1136+0.89 
1184+0. 91 
1222+0.92 
1731+0.99 
1782+0.99 
1821-^1.00 
1887  +  1.00 


509 
459 
499 
638 
69S 
8ql 
957 
II97 
1277 
12S5 
1795 
1835 
1895 
1955- 


j-29 
I -69 

-28 

-14 
8 

+27 

+46 

+61 

+93 
+63 

1+64 

1+53 
1889    ',  +74 

+  67— nj 


1780 
1823 


+  49 

+41 

+  68 
+  67, 


Here,  it  is  evident,  the  observed  distances  are  sj-stcmatically  too  <jrcat  for  the 
meau  i)ha.ses,  and  it  is  impossible  to  satisfact..rily  eliminate  this  errf)r  in  the  way  we 
have  ..enerallv  adopted  in  the  case  of  these  (u-lipses,  because  there  is  a  gap  near  the 
be.nnnin-.'  of  "the  eclipse,  correspoudin-  to  the  best  observations  near  the  end,  while 
the  gap  between  o"  55"'  and  i"  14'"  c.rresponds  to  tlie  best  series  near  the  beo'iminif.'. 
The  .systematic  error  in  tpiestion  seems  to  l)e  zero,  or  even  negative,  near  the  middle 
of  the  eclipse.  Under  these  circuni.stances,  ..ur  best  cour.se  seems  to  be  to  correct  the 
observetl  di.stances  by  an  empirical  formula,  and  to  give  most  weight  to  the  observa- 
tions near  the  extreme  phases.     We  choose  the  correction, 


(  //>— 1400V) 


l,y  applying  which  we  torm  the  second  column  of  observed  di.stances  and  of  correction 
to  the  tabular  distances.  Where  this  second  column  is  not  formed,  we  have  corre- 
sponding observations  betitre  and  after  the  midille  of  the  eclii)se. 

(jonmienciiig  n(»w  with  tlu^  consideration  of  the  contacts,  the  considerable  mag- 
nitude of  the  eclipse  at  the  ol)serv('d  moment  of  contact  niuih-rs  it  suspicious;  still,  as 


246 


RESEARCllKS  ON  THE  MOTION  OF  THE  MOON. 


IlEVEi,n-s  siivs,  it  Wiis  (.1  (Served  "accuratissiine",  1  luive  not  felt  jiistilied  in  rejectinj-- 
it.    Coinbininj--  the  observution.s  of  first  and  last  contacts  in  the  usual  manner,  we  find: 

'5f  +  33",  "t-  =  2. 

The  mean  of  the  seven  (djservatioiis  following-  lirst  contact,  nsin-i'  the  corrected 
distances,  gives 

'5i  rr  +  26",  \vt.  =:  i. 

The  mean  of  the  tin-ee  observations  precodin<>'  last  contact  "-ives 

Sf  -  +  53",  wt.  =  2. 

The  result  of  the  intermediate  observations,  five  on  each  side  of  the  middle  of 
the  eclipse,  in  which  the  distaiu-e  exceeds  890",  tornied  by  takinj-'  the  differences  of 
the  correspoiuling-  measures  on  each  side,  is: — 

'5i  +  36",  wt.  =  3  ; 
the  mean  result  of  all  tlie  measures, 

'5f  =  +  3X". 

Considering  the  uncertainty  of  the  times  and  of  the  measures,  the  probable  error 
of  this  result  cannot  be  uuu-h  below  10". 


Eclipse  of  1654,  Aiii^itst  11,  obscnr,!  by  Wai.tkkilis  at  Aix, 

Moon's  somi-tliaiiielfr  at  licginnin),'  .  970' 
Moon's  si'mi-diainetcr  at  end  .  .  .  973" 
Sun's  semi-diamolcr g^g" 


Obs.  All,  Local  Mian    Tahnlar  Dist.  of    Observed 
of  0.  Tinii;.  Ctiuris.  Distanru. 


35 
30 
38 
39 
41 
41 
42 
43 
45 
47 
48 
49 
50 


30 
15 
35 
45 

10 

35 

35 

b 

35 
"4 
lo 
7 
20 


// 

HI 

2(1 

24  g 

32.0 

- 

I .uoiW 

32.0 

211 

29-3 

30.2 

- 

"■'W 

29 -3 

20 

42-7 

25-3 

- 

0.94 

24.1 

20 

4').  5 

22.8 

- 

0.8,, 

22. S 

20 

57.8 

20.0 

- 

0.S2 

21.5 

21 

"•3 

13.3 

- 

o.So 

IS.S 

21 

(1.2 

17-4 

- 

0.72 

17.5 

21 

9.3 

16.5 

- 

0.67 

If).  2 

21 

24-3 

132 

- 

0.32 

l3-f> 

2r 

34.9 

12.2 

-f- 

0.04 

12.3 

21 

40.  y 

12.4 

+ 

0.25 

10. () 

21 

47-2 

13.0 

+ 

o.4f, 

I3.f' 

21 

55-3    1 

■  4-3 

+ 

0.66 

■4.9 

! 
Obs 

.All. 

Lo<:aI  Mcai 

Talnilai   DisI,  of 

1 
Obsirvid 

of©. 

Time. 

f't'iilrcs. 

Distance. 

.i 

. 

0 

. 

//        w 

» 

] 

-        — 

0.0 

1    51 

10 

22      1,1 

15.f1   T   0.781!) 

lfl.2 

+    o.f) 

0.9 

■    52 

2 

22      7.2 

17-1    +  0.86 

•7.5 

+  "•4, 

1.3 

52 

2(, 

22    10. 1 

iS.o  -)-  0.89 

18. 8 

+  0.81 

0.0 

i    -^ 

12 

22    15.(1 

'9-5   +  u.y4 

20.2 

+  0.7' 

'0 

1    53 

50 

22    20.6 

21 . 1    -1-  o.r)7 

21.5 

+   0.4 

0.5 

54 

21 

22    24.7 

22.4    +    I.otl 

22.8 

+  0.4 

O.I 

54 

55 

22     2i}.2 

23-9  +    1.02 

24.1 

+   0.2 

0.3 

55 

20    j 

22     32.7 

25.1    +    1.03 

25-5 

+  0.4 

0.4 

55 

33    i 

22     34.5 

25.7   +    1.04 

26.8 

+    I.I 

0.1 

55 

58    i 

22     38.0 

26.  S   +    1    .^^ 

20.1 

+    1-3 

4.5 

5f> 

18 

22     41.0 

27.9   +    1.05 

21).  4 

+    '    5 

0.6 

57 

t 

22    47.4 

3<'l     t-    1.07 

3'i.7 

f   0.6 

O.f)  j 

57 

20    1 

22     50.4 

31.2    +    1.07 

32.0-n.. 

+  0.8 

RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


247 


Tliorc  is  no  (ivuliMV-o  of  systoinatic  cmtr  in  tlio  determiniition  of  tlu;  pliascs.  If 
wo  tiiko  tlio  snni  of  all  tlie  o([nfttions  in  wiiicli  tlic  coolKcicMt  oxccods  0.6,  tlio  cimtacts 
o.\('('j)tO(l,  Avc  have: — 

Sum  of  seven  ('(jiiations  near  l)o<iinnin<i'        3.<S3  f5f  —  o'.3 
Sum  of  tliirteeii  e(|uati(»ns  near  end  .     .      12.36  g'.o 

Sum  of  all I  S.I  9  9'. 3. 

From  wliieli  we  find '5*  r= +  o'.5i.  Supposin-;-  «,,=:  A  «,,  the  contacts  alone  will 
j>-ive  '5f  =  +o'.53.     We  may  therefore  [)iit,  as  the  result  of  this  eclipse, 

,5t=4-3i". 


Er/i/'Sf  of  i66r,  March  29-30,  nhrnu-d  hy  IlKNKr.ius. 

Moon's  appiirciil  sonii-iliamcler  ;\t  licginniiii;     .      ii»0".o 
Moon's  apparent  s;Mni-cliaini'in  al  und      .      .  i(x)6  ".5 

Sun's  apparent  semi-diameter 059  -'J 


Local  M 

ean 

Tahniar  Dist.  of 

Observed 

Corr.  to 

Local  M 

ean 

Tabular  Dist.  of 

Ol)Served 

Corr.  to 

Time 

s 
10 

C(  ntres. 
IQcjI  —  1 .031I1 

Distance. 

Iq()()  — 'i| 

Tab.  Dist. 

-   25 

Time 

h       lit 

23     53 

47 

Centres. 
1014  +  o.SSih 

Distance. 

Tab.  Dist. 

/;       III 
22      K) 

967 

-   47 

20 

33 

KJ54  -  1.03 

lq2() 

-    2S 

0      4 

30 

1235  +  o.yy 

1247 

+    12 

21 

I 

11)44  -  I -02 

I  l)Of) 

-   38 

6 

25 

1274  +  1. 00 

1307 

+   33 

22 

5> 

Ii)03  —  1 .02 

1 866 

-  37 

8 

12 

1312  +  1.02 

1367 

+   55 

24 

if) 

l8(jf)  —  I.OI 

1826 

-   40 

'5 

12 

1472  +  1.05 

1527 

+  55 

25 

30 

i32g  —  I.OI 

1 7</i 

-   33 

16 

20 

1498  +  1.06 

1547 

+    40 

27 

24 

1784-  I.CX) 

1746 

-  3S 

'7 

5<: 

1533  +  I  .of' 

1 5^)7 

+  34 

V> 

24 

1 706  —  0.  i)() 

1686 

—    20 

■0 

4 

1561  +  1.07 

1607 

+  46 

4' 

30 

1438-0.93 

1447 

+      0 

'0 

0 

1579  +  1.07 

1627 

+  48 

50 

>0 

1236  —  0.86 

1267 

+   31 

20 

34 

1596  +  1.07 

1637 

+   41 

5S 

50 

i'54  -  0.75 

1067 

+    13 

22 

4 

1632  +  1.07 

1667 

+   35 

50 

55 

1035  -  0.74 

1027 

-     8 

22 

58 

1654  +  1 .08 

1687 

+   33 

23       I 

40 

1003  —  0.71 

007 

-     6 

23 

48 

1674  +  1.08 

1707 

+   33 

2 

36 

i)SS  -  0.70 

047 

-   4t 

25 

6 

1705  +  I .oS 

1727 

+  22 

4 

32 

055  -0.65 

007 

-   48 

26 

7 

1730  +  1 .08 

1767 

+   37 

0 

2 

S78  -  0.54 

S47 

-    31 

26 

45 

1745  +  i.oS 

17S7 

+  42 

12 

S 

837-0.4P 

S37 

0 

27 

5fi 

1774  +  I. 00 

1S07 

+  33 

13 

22 

824  -  0.42 

827 

+     3 

2S 

53 

1798  +   I.oq 

1847 

t-   40 

■0 

14 

75S  —  0.22 

747 

—   II 

30 

21 

1832  +  1 .10 

1886 

+    54 

2t 

iS 

744  -0.15 

727 

-    17 

33 

26 

1907  f  1. 10 

1966— '1 J 

+   50 

40 

41 

8o()  +  0.61 

827 

+   18 

Combinin-;'  the  seven  pha,.ses  foUowin;^-  the  beginning'  with  the  corresponding  ones 
preceding  the  end,  ve  fnid  ^5*  —  +  34".  The  contacts  alone  give  <5f  —  +  48".  Giving 
th(^  mean  result  from  contacts  the  weight  of  two  pairs  of  observations  of  i)hase,  wo 

have: — 

Af  =  +  37". 

The  other  i)hase.s  do  not  correspond  to  each  other,  and  the  agreement  of  the 
.sevtMi  pairs  we  have  used  is  .so  good  that  it  thtes  not  seem  necessary  to  dist-uss  them. 


248 


RESKARCUES  ON  THE  MOTION  OF  THE  MOON. 
Eclipse  of  1666,  yitly  1,  ohscrrrd  by  Hkvki.us, 

Mdoh's  .ippaicnt  sunii-ilianicicr  at  lif.niiininR  .  1)44". 8 
Moon's  appareni  suini-cliaim'tci  al  v\v\  .  .  .  <m)".i) 
Sun's  appareni  semi-dianietei 'M-\"fi 


Local  .\ 

can 

Talnilar  Disl.  ol 

OhsiTvcd 

Corr.  to 

Local  M 

can 

Talnilar  r)ist.nf 

Observed 

Corr.  to 

Time 

s 

("cnlrcs. 

Distance. 

Tab.  Dist. 

/; 

riinc 

s 

Centres. 

Distance. 

Tab.  Dist. 

//  m 

»• 

U)        1 

17 

Ig04  —  o.c)2(W 

l88t)  — n, 

-  15  — "1 

'9 

59 

24 

614  -  o.isi'i 

5S5 

-  29 

3 

17 

1849  —  O.IJI 

1S30 

-  '9 

20 

1 

32 

602  —  0.07 

57) 

-  28 

f. 

10 

1770  —  n.qo 

1772 

f-  2 

4 

52 

5S7  -t-  0.09 

5S2 

-  5 

8 

'7 

I7II  —  0.()0 

1713 

+   2 

12 

'7 

617  +0.39 

602 

-  15 

10 

37 

1649  —  o.Sq 

■651 

+   5 

17 

12 

667  +  0.57 

672 

+  5 

If. 

44 

1487  -  0.87 

1516: 

+  29: 

23 

17 

760  +  0.72 

751 

-  9 

20 

46 

1383  -  0.S6 

1359 

-  24 

25 

23 

798  +  0.76 

79' 

-  7 

23 

37 

1311  -0.84 

1300 

—  II 

33 

55 

958  +  0.86 

96f) 

4-  8 

27 

22 

1216  —  0.82 

1 201 

-  "5 

3f' 

I 

looi  +  0.88 

1027 

+  26 

29 

30 

1 163  —  0.80 

1155 

-  8 

42 

12 

1134  +  0.92 

I145 

+  II 

33 

40 

1065  -0.77 

Iof)4 

—   I 

49 

6 

1285  +  0.95 

1322 

+  37 

37 

37 

971  -  0.73 

946 

-  25 

51 

59 

1354  +  0.95 

1381 

+  27 

42 

42 

866  -0.65 

829 

-  37 

53 

19 

1385  +  0.96 

1422 

+  37 

43 

52 

841  -0  63 

799 

-  42 

20 

56 

44 

1466  +  0.96 

1461 

—  5 

45 

32 

813  —  0.60 

769 

-  44 

21 

0 

2 

1544  +  0.97 

1539 

-  5 

4S 

17 

754  -  0.54 

739 

—  If, 

4 

11 

1644  +  0.9S 

1676 

+  32 

49 

53 

729-0.49 

7H 

-  18 

5 

22 

1O73  +0.98 

1710 

+  43 

51 

47 

702-0.44 

684 

-  18 

7 

25 

1721  +  0.93 

1761 

+  40 

54 

12 

6(17  —  0.36 

632 

-  35 

9 

7 

1761  +  0.98 

1815 

4-  54 

57 

2 

636  —  0.25 

602 

-  34 

1  '' 

12 

40 

1849  +  0.99 

1894-n.j 

+  45-"^ 

Tlio  coiitiicts  alone  here  yive 


r5f  =  +  36". 


'rh(>  fdiir  observations  follo\viii<>'  first  contact,  combined  with  tho  corrospondinfr 
t'oiu'  precedin}^'  last  contact,  ji'ive 

Se  —  -f  24. 
Tho  remaining  obsei'vations  in  which  the  distance  exceeded  900"  give 

f5£  =  +  22",  or  <5i— +15", 

according  as  wo  Inchido  or  reject  the  donbtfnl  fifth  observation  of  phase.     Tho  most 
])robable  resnlt  o\'  all  tho  observations  is. 


<5*=  +  25". 


RESEARCIIKS  ON  THF,  MOTION  OF  THE  MOON. 
Eclipse  of  1C76,   yiiiie   10,  ohsi-ireil  hy  I'l.xMSi  kid  nt  Giriin.'uh. 

Moon's  apparent  srmi-diamctir  at  first  olisorvalion  .  S()4".() 
Moon's  apparent  senii-iliamuler  at  last  i>l)si'rvalii)n  .  8()f>  "o 
Sim's  senii-ilianieter i)-l5   ■" 


'  i  Corr.  to 

Mean  Time      ''«!  «'l-'>- Dist.  of    Observed  Dist.    .,.^,,,,,^^ 
Centres.         :       (by  cuspsj.       ;     |jj^, 


249 


h  m 

20  2 

20  II 

20  38 


If) 

4 

32 

"J 


1751  —  o.fifjiW 

1655  ~  o.fM 

1513  -  oM 

1244  —  0.22 


20  16  2q  1447  —  0.551W 

20  18  58  '  I416  —  0.53 

20  25  53  \  1339  —  0.40 

20  26  53  '  I32q  —  0.45 

20  33  4  i  1277  -  0.3S 


I73f> 
1 039 
I4')5 
1282 
(liy  dir.  ineas.) 
1433 
14" 
1361 
1308 
12S1 


-  15 

-  If) 

-  IS 


An  exainiiiation  of  Fi.AM^i  i;r.ii's  ol)served  semi- 
diameters  of  ilie  sun  shows  that  liis  micrometer 
measures  of  that  element  rei|uirea  correction  of —  7". 5 
for  irradiation    when  ilie   lonf?  telescope  was  used. 

+  38  I  and  — 14 '.3  wlienthesliorl  one  wasused.  Thesecor- 
rerlinns  have  lieen  applied  in  llie  colnmn  of  oliservcd 

_         '     distance  when  necessary. 

-  5 
+  22 

—  21 
+     4 


At  the  timtt  of  the  bist  meiisum  of  the  (listancc  of  (Misps,  the  eclipse  mis  so  far 
iidvaiieed  that  110  rehahh;  residt  coiihl  l)e  obtained  from  tlie  measure.  .AForeover.  the 
diseordaiice  of  the  result  is  such  as  to  indicate  some  mistake.  The  results  from  the 
other  measui-es  nuiy  fairly  receive  the  respective  weio'hts  4,  3,  and  2.  The  discord- 
ance of  the  third  measure  of  phase  is  also  so  <>-roat  as  to  <^-ive  rise  to  a  suspicion  ot 
some  error  in  the  reciu'd.  The  error  is  in  fact  between  30"  and  40",  whereas  the 
probable  error  of  Fi.amstf.ek's  measures  of  the  sun's  semi-dianu-ter  tUtes  not  in  gen- 
eral exceed  3"  or  4". 

From  the  three  first  measures  of  distance  of  cusps  with  the  wei<,'hts  assifjued,  we 

have, 

''if  rz+ 2  5".o. 

The  suni  of  all  the  etpiations  <riven  by  the  phases  is, 

2.37 '5/- rz  + '4  ":   •'• '">f  =  + ''^"• 
Rejectino-  the  third  measure,  we  shall  have, 

I.Ql    ''if  =  +  36;     .-.  ''if  =  +   10". 

Tiie  residts  from  measures  of  distance  of  cusps  near  the  be«i,'innin<;-  of  an  ecli|)se 
ought  to  1)0  prettv  accurate,  while  the  discordance  of  the  ineasiu'es  of  phase  renders 
their  results  uiu'ertain.  I  t!;,-refore  consider  th(^  most  probable  result  from  thiN  eclii)se 
to  be. 


(5f  =  +  23"  ±6' 


32 T.J  Ar.  2 


250 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

Eclipse  of  i()?>^,  yuly  \2,  ohsencd by  I'I.amstked. 

Moon's  a|)p;irciit  somi-diaiiR-ltr  .11  hijjinniiiK  .  946'  .7 
Moon's  apparent  scnii-diamctcr  :it  ciiil  .  .  .  943". S 
Sun's  suniiUiameler 944".6 


Mean  lime 


■7  44 

25  39 

42  5') 

47  Sf) 

I  1  = 

5  21' 

6  23 
8  6 
S  34 

14  2 

15  7 
19  19 

21  59 

26  10 
30  13 
3fi  27 


Tabular  Dist.  of 
Centres. 


1891    —  o.g&df 

1654   -  0.94 

1352  —  0.90 

1252  —  o.S; 

'))7  -  ".75 

937    -  0.70 

923  —  0.69 

899   —  O.flf) 

St)  I   —  0.65 

S21   -  0.54 

781   -  0.45 

770  -  0.42 

754  -  0.33 

73fi  -  0.19 

734  -  0.04 

763  +  0.15 


OI)served 
Distance. 


I8f)2 

1655 

1334* 

1241 

1005 

945 

90 1  * 

S69* 

SSfi 

827 

741* 

7f>S 

724* 

73S 

733 

768 


Corr.  to 

Tabular 
IJisi. 


J! 


-  29 
+     I 

-  18 

-  1 1 


-  22 

-  30 

-  5 
+     ft 

-  37 

-  2 

-  30 
+  2 
+  4 
+     5 


Micrometer  measures  of  "pars  lucida", 


Mean 

ifiie. 

Tabular  Disi,  of 
Centres. 

Observed 
Distance. 

Corr.  to 

Tabular 

Dist. 

//     /// 

r 

„ 

M 

3    39 

35 

786  +  o.26(!i 

797 

+        II 

41 

54 

811    +  0.33 

82ft 

+    >5 

46 

21 

8ft5   +   0.43 

885 

+    20 

5" 

39 

931    +  0.53 

944 

+    13 

53 

4 

973   +  0.57 

io<i3 

■V   30 

59 

17 

1087   +  0.66 

1121 

+   34 

4      2 

>9 

II48   +  0.70 

tl8o 

+   32 

5 

5 

1205   +  0.72 

1240 

+   35 

12 

52 

■377  +  0.78 

'417 

+  40 

20 

2S 

155ft  +  0.83 

•SftSf 

+   12 

20 

40 

1561   +  0.83 

1594 

+  33 

23 

34 

1632   +  0.84 

ift4of 

+     8 

25 

5f' 

iftgo  +  0.85 

1741 

+   51 

20 

52 

1714   -i-  0.S5 

'736f 

+   22 

29 

2(1 

1778  +  0.36 

1829 

+   51 

32 

42 

1859  -r  0.87 

1888 

4-   29 

f  From  measures  of  cusps. 

There  is  dearly  ii  systeiiiatie  error  in  the  measures  ttf  ])hase,  renderinj^-  it  neces- 
sary to  eonipare  phases  as  nearly  equal  as  possible  (ni  eaeh  side  of  the  middle.  This 
comparison  gives  the  etjuations, 

0.87  rSi—     9",  \.l2  6t  —  22" 

1.08 

I.2-! 


5 

1-59 

46 

5 

1. 78 

43 

I. Si 

80. 

The  solution  of  these  equations  gives 

t5.=  +  25". 
Tlie  micrometer  measures  of  "pars  lucidae"  before  the  middle  of  the  eclij)se  give 

.5f  =  +  38".   . 
The  three  measures  of  cusps  near  the  end  give 

.5.  = +17". 
The  most  probable  result  fi-om  all  the  observations  is 

«Jfc  =  +  24"±4". 


RKSEARCHF.S  ON  THE  MOTION  OF  THE  MOON. 

Eclipsi'  "/  1684,  yll/^  \2,  ol'sarci  hy  La   Hink  iU  I'um. 


MoDIl'.S 

ippaicnt  seini-iliamcler  at  boRinninK     .     ()4f>".7 

Moon's 

ippaienl  senii-<liaiiieter  at  end     . 

.      .     943'  .2 

an 

Sun's  St 
Fahiilar  Distance 

nii-diametei   .... 

.      .     044".& 

,ocal  Mt 

01)servecl 

Corr.to 

I.oc 

>1  Mean 

"T 

Falnilir  Distance  Observed 

Corr.to 

Time. 

uf  Centres. 

Distance. 

lab.  Disl. 

') 

"ime.       i 

of  Centres. 

Distance. 

I'ab.  Dist. 

h     in 

2     30 

s    \ 

23  i 

I(j34.8  -  o.(j8  Uj 

l8qi.3 

-  43-"! 

h 
4 

m      s 

18    57  ; 

1130. 1  +  o.73iI( 

II 
1173 

+  34 

35 

16 

i.SaS.l  --  o.(j7      ; 

I7<)8 

-  30 

23     37  ' 

1244.4  +  0.77 

1284 

+  40 

41 

6 

1 6()() .  4  —  0 .  ()6 

1673 

-26 

20     57  , 

1393.8  +  0.82 

1417 

+  23 

43 

16 

1652. 1)  —  o.()6 

lf>35 

-  '7 

3'>     57 

1566.5  +0.84      i 

1607 

+  40 

4'J 

16 

1521.0-  o.()5 

1407 

-24 

43     37 

1736.6   +   0. 87          ; 

1778 

+  4' 

53 

6 

1433.6  -  o.(j4 

1418 

—  21 

48  27 ; 

1862.8    +   O.H9 

1887. S 
From 

+  25 -flu 

5f> 

46 

13?')-')  -  "-yJ 

1325 

-  35 

1 

1 

meas.  of 

3       3 

6 

1227.0  -  0.90 

iigb 

-31         1 

j 

cnsps. 

9 

16 

1102.3  -  0.87 

1077 

-25 

37     Sf' 

1776.4  —0.97''' 

1707 

-69 

15 

46 

t)7(j.  I  —  0.81 

075 

-    4 

45       f' 

1611 .8  —  0.96 

I5»7 

-  25 

23 

6 

852.4  —  0.71 

841 

~  '2 

54     2f' 

1409,6  —  0.93 

1304 

-  16 

26 

26 

603.2  —  0.65 

,      784 

1-19 

50     3f) 

12()9.8  —  0.92 

1301 

+    I 

33 

26 

7l(j.i  -o.4() 

1       708 

-..   .;  3 

7      6 

1145.8  -0.88 

1081 

-65 

41 

26 

66g.o  —  0.22 

;    660 

r  '^ 

12     51 

1032.6  -0.83 

1025 

-    8 

45 

6 

666.2 -O.oS 

665 

I- "    ,  4 

21     37 

119S.4  +  0.76 

1229 

+  31 

56 

7 

736.4  +0.32 

i     765 

1  +  29 

25     57 

1298.4  +  0.79 

1331 

+  33 

4        I 

47 

811. 6  +  0.47 

835 

;  +  13 

33     18 

1475.4  +  0.S3 

1502 

+  27 

5 

27 

871.0  +  0.55 

1     879 

+     8 

42    27 

1706.6  +  0.87 

1727 

+  20 

10 

7 

(J56.0  +  0.63 

1       075 

+  >9 

•i 

Trejitlng  tlio  contacts  in  the  usual  way,  tlie  result  is, 

.^.=  +  31". 

The  sum  of  the  eleven  etiuations  from  phases  following  first  contact  in  which  the 
coefficient  of  6e  exceeds  0.5  is, 

9.65  A-f=  244"-.  .•.''^  =  +  25"- 
The  sum  of  seven  phases  preceding  last  contact, 

5.21  r^f  =  205":  .-.  '^f  =r  +  4o". 
The  measures  of  cusps  near  begimiing,  giving  doul)le  weight  when /)  >  1600", 
give  the  result, 

r5*zr  +  37"- 

Those  near  end  give 

'^f  =  +  32"- 
The  most  probable  mean  result  is, 

Se-  +  Z2"  ±2". 


RKSEARCIIICS  ON  THE  MOTION  UK  Tllli  MooN. 

Ei/i/'xr  0/  i6Sj,  May  w ,  ,th.u-nr,l  hj  Fiamsikkh. 

MiKin's  a|)|i:M()iil  senii-iliariii'ltr  al  liCKiniiiiiK  ,  (^55".^ 
Miion's  :i|i|iai('nl  scnii-iliamcler  al  end  .  ,  i)54".3 
Sun's  ;i|i|iai(iii  vciiii-diamcU'r iM4".'i 


MciM  Tinic.    Tahiilar  Di-^lanic  of  Ciiiiiis. 


OhscrMcl 
llisiaiu'i'. 


Mrairiin.c.    -lal.ul.u   Dislan.c  i.f  (•.■iilrrs.      "'""'"■'"I 

iJisiaticu. 


//     m 

s 

" 

'     '3 

3 

"P5 

.      . 

15 

•JI 

1885 

- 

o.i8itf 

+   i).ijS( 

ilH 

.871.2 

17 

') 

1S77 

- 

0.17 

-1-  0.1)8 

1S51J.7 

22 

5 

HW 

- 

0. 11 

+  11.  w 

1G31.2 

28 

31 

1825 

- 

11.1)2 

+   i>..)y 

lSift.7 

31 

53 

iSr7 

0.(J<) 

■(-     I.  IK) 

1810.5 

35 

27 

I8l2 

4- 

0.07 

t-     0.()CJ 

l8o4.y 

3S 

3 

1812 

+ 

0.  lu 

+    0.(J() 

1804.8 

k    m 

s 

t* 

,, 

I    38 

43 

1812    (-  (1. 1 1  il 

'     1     0 . 9(j  /  il  H 

1804.8 

411 

4i> 

1S13  i-  11.13 

+    n.,j,j 

1807.4 

44 

47 

1820     f    1).  icj 

+   0.98 

1816.7 

48 

3 

1830  +  0.23 

f    o.()7 

1832.0 

54 

1 

1855    +  0.30 

+  0.95 

1858.9 

55 

43 

1SO4    -f    0.32 

-(-  0.95 

1870.3 

2      (J 

"3 

1892   +  0.38 

+  o.<J3 

1898.9  — (1; 

0 

'^ 

1893   +  0.38 

+  0-Q3 

1898.9  — (1; 

This  cclii.so  iiiul  tlio  next  (.110  wuro  ori^-iuiilly  coinputcd  witli  the  liopo  tluit  tlioy 
would  "iivc  ii  valiinblc  coiTcctioii  t..  the  loiioituilc  of  the  inooii'.s  iioih-.  Thcv  fire  too 
siiiiill  to  he  of  iuiy  ii.sc  for  (h-tcnniiiiiio-  the  loii^-itiuh'.  Hut  it  secin.s  that  iii  tlic  two 
echjisos  a  chaii-ic  in  the  node  will  have  the  .same  etieet  011  the  di.stuiifo  of  centres, 
and  tlu  systeinatie  errors  in  the  observations  may  lie  such  that  no  jrood  result  can  lie 
obtained.  ^  1  therefore  make  no  use  of  the  eclipses,  but  present  the  data  for  the  u.se  of 
any  investigator  who  may  choose  to  discuss  them. 


Eclipse  of  16S9,  Sepli-nihrr  13,  ohseircil  by    lM..\MsrKKl), 

Moon's  apparciil  scnii-diaiiulfi  al  IjugiiiniiiR  .  923  '.o 
Moon's  apparent  st'nii-dianit'lrr  at  end  .  .  .  920". 4 
.Sun's  appari'iii  scmi-dianittcr 955". 8 


lean  '1 

iiiic. 

Taliu 

ar 

Distance  o(  Cenlres. 

Observed 
Distance. 

Mean  Time. 

Tatnilar 

Distance  of  Centres. 

Oiiserved 
Distance. 

//     ;// 

.»■ 

" 

1, 

m 

i        ,/ 

3  24 

57 

1884 

— 

0.34  ■'' 

■t- 

0 .  90  / 1)  (/ 

1843.4-,,, 

4 

8 

57 

1693    + 

o.26,If 

+  0.93; 

,W7 

'701.3 

37 

7 

1762 

— 

0.20 

+ 

0.94 

1764.0 

11 

35 

1706   + 

0.30 

+  0.92 

'712.5 

40 

'  7 

1736 

— 

0. 16 

+ 

0.95 

1727.5 

15 

39 

1732   + 

"•34 

+  0.90 

'740.1 

44 

43 

1708 

— 

0 .  og 

+ 

0.96 

1703-7 

18 

57 

175')  + 

o.3'J 

+  0.88 

1763.1 

48 

37 

IU91 

- 

0.04 

+ 

0.96 

1687,9 

21 

31) 

1784   + 

0.43 

+  0.86 

1792-9 

53 

51 

1676 

-f- 

0.04 

+ 

0 .  96 

11176.1 

24 

21 

1810  + 

"■45 

+  0.85 

1818.1 

4      3 

57 

1676 

-1- 

0.19 

-t- 

o-iJS 

1674 -3 

28 

57 

1863   + 

0.49 

+  0.82 

1876. 2-nj 

7 

5 

1CS6 

-\- 

0.24 

+ 

0.94 

.685.0 

29 

3 

1864   + 

0. 50 

f  0.81 

1876.2— a.j 

RESKARCllES  ON    IIIK  MOTION  OF  TIIK  MOON. 
/iV///.tc  "/  tdcj').  Sf/<f,mhi-  23,  ,>/'S,'nri/  /•¥  I. a    IIikk  ,1/  /'ii/is. 


253 


Mddii's  sciiii-iliiitiii'ti'i  :it  lii'i(iiiiiiii.u 
MiKin's  scriii-cliaim-liT  ;il  end      . 
Sun's  Sfiiii-ili;inH'ii'r 


I 


')''3".5 
c)W.".!i 

,,5H'.4 


Paris  MiMn    Tabular  DiMam-iOl.scrvHli    Corr.  to     '  Paris  Mian    1  ..l.ulai  I'i-^i.niM    Ol.^dv,,!     Curi.iu 
Tinii'.  i.fCcMlrcs.         Distanrr    Tal..  Dist.    ,       Tiitif.  ..fCcnlM^^  DiMan.r      lal.,  I)is|. 


JO 

ni 

7 

') 

I(Jj0.2-  I  .01  1'' 

11)21. () 

„ 

-14.3 -" 

') 

34 

1872.1-1.')! 

1842.1 

-3".2 

12 

"') 

1800.0—  1  .111 

1 762 . 3 

-37.7 

I(J 

III 

ifi()().3  —  1 .1X1 

16S2.5 

-16.8 

"J 

21 

1616.4  —  1 .00 

1602.7 

-13.7 

22 

35 

1532.1j-1.iKi 

1522. 1) 

-10.0 

24 

37 

1480. 7-0. ()ij 

1443.2 

-37-5 

2S 

10 

I3()0.3-o.c)8 

I3f'3.4 

-26.CJ 

3" 

57 

1320. 1— o.ijS 

1283.6 

-36.5 

33 

55 

1245. 4-0. y7 

1203.  (J 

-41.5 

37 

7 

1166.0  —  0.1/1 

1124.1 

-41. IJ 

41  > 

4^' 

1076.7-0.y5 

1044.3 

-32.4 

44 

",i 

()<jl.4-o.y3 

,)64.6 

;  -26.8 

47 

53 

IJ06.7— U.()I 

884. 8 

1    -31. IJ 

51 

14 

82().  1—0. 8(j 

805 . 0 

-24.1 

55 

II 

7411.6  — 0.S5 

7  =  5-2 

i    ->5.4 

S'l 

2 

658.2-0.80 

fi45.5 

,   -12.7 

21 

3 

3 

573.0-0.72 

5''5 . 7 

-12.3 

7 

57 

4')I. ')-'>■  51J 

486.0 

-   $■<) 

15 

'7 

402.5  —  0.23 

406 . 2 

^■  3.7 

22 

4» 

38S.4+0.a6il' 

406 . 3 

+  17.9 

2ij 

14 

450.2  +  0.63 

486.3 

+  36-1 

35 

30 

538.CJ  +  0.80 

566.2 

t-27.3 

3') 

28 

61 1 .4  +  0. 88 

646.1 

+  34.7 

43 

18 

I1S7.2  1  O.IJI 

726.0 

+  38. » 

41) 

33 

818. 3+0.1)7 

8S5.1) 

+  67.6 

54 

7 

ijl8.o+o.i)ij 

1J65.CJ 

+  47. 1) 

5S 

4 

1005 .4  t-  I. oil 

1045. '< 

+  40.4 

2 

56 

11 15. 2  + 1. 01 

1125.7 

+  10.5 

6 

3S 

Illji).3+l.l)2 

1 205 . 6 

+  (.,3 

>) 

46 

I27o.(j  +  i.o3 

12S5.5 

+  14-6 

12 

57 

1344.4l-l.03 

1  3^'?  •  5 

+  21.  I 

16 

5(> 

1435. 3+1.03 

1445-4 

+  10,1 

2IJ 

55 

1504.0+  1 .114 

1525   3 

+  21.3 

24 

17 

16114. 8+1. o| 

1605,3 

•    +    0.5 

27 

44 

16S4.4  +  1.04 

1685.2 

+  0.8 

3> 

10 

1763.7  +  1.04 

1765.1 

+    1.4 

33 

48 

1824.6  +  1,04 

1S45.0 

+  20,4 

37 

9 

lijoi  .8  hi. 04 

1IJ24.IJ 

+  23,1 

Till)  ruutacts  give 

<5fzz  -f  20". 2. 
'I'hc  16  moiisuros  uf  pliii.sc  followiuf-'  lii'st  L-oiitiiet, 

15.23 '5f  =  426";  .■.<'it  =  +  27".g. 
Tliu  16  uiuiLsures  of  pluisc  procodiiij;-  last  coiitiict, 

1  5.87  'Sf  =  364";     .-.  <U  =  +  22".9. 

Till)  mean  result  is, 

r5f  =  +  24".8  db  2". 


'■54 


RESEARCHES  ON  TIIIC  MOTION  OF  THE  MOON. 
j5'i7//..r  ,'/  fjo6,Miv  i\,i>/>sc>ra/  h  I, a  Hikk  <?/  JUris. 

Moon's  apparent  senii-diainelcr  at  begiiinini;  .  ioo3".() 
Moon's  apparent  senii-dianicler  at  end  .  .  .  loofi'  .1 
Snn's  apparent  semidiainctir 04')  "•> 

Paris  Mean    Talnilar  f)isian<e  Ohserved    Corr.  lo      Paris  Mean    Taluilar  Distance  Observedl   Corr.  to 


of  Centres. 


i(j5ij.o  —  i.oSiIi 


[Jisia 


Tal).  Disi 


.if  (■ 


Disiance.lTali.  DIst. 


U  37  1275.0  -  1.06 

4S  37  '   1I57-S  -  t.05 

51  37  1070.4  —  1.05 

'I  '2  i)'J5-5  -  1.04 

56  5S  915-9  -   1.03 

57  4S  3(12. 1  —  1.03 
3  53  719.9  -o.'J'i 


r932:  -  27 

1254  —  2t 

•124  '  -  34 

104S  —  22 

972  -  24 

896  —  20 

739  (-'53) 


50        8         670.4  +  I.I2.1' 
M     23       703.0   t-  1.12 


52     4S 


74>-4  +  I. 12 


54    23       783,9  + 


5f' 


S30.4 


1. 13 


701 


19 


5     18       tSo.; 
<■'    33       645.9 


1.98 
>-97 


7  48  <i'i.3  —  0.9O 

9  iS  57"-4  -0.95 

10  48  530.4  -  o.,^3 

I:!  10  494.3  -  0.91 

'3  43  452. 


24 


■  0.88 


15  11  417.3  —  o.Sf 
'7  3  372.3  -  ".79 
'S     43       333-9  -  "-72 


Cf>3  -  27 

625  —  21 
587 

549  -    21 

511  -    19 

473  -   2T 

435  -    17 

398  -    19 


57  28  860. ()  +  1.13 

59  3  9"<)-3  +  1. 13 

0  23  945.2  (-1.13 

1  53  9S5-7  -t  I- 13 
3  23  1026. 


4-  I -.3 


20   43 


292 


■  0.62 


■■■■7    38 


256.6  —  0.44 
214.0  +  0.20 

31  53  '  233-0  +  0.62 

32  53  I  260.8  +  0.80 
35  4  300-5  +  o-9> 
3C>    35  I  333-2  +  0.97 

33  i6  '  369.8  -(-  1. 01 
30  38  j  401.7  +  1.06 

41  18  j  442.3  +  1.06 

42  58  [  483. 8  +  1.07 

44  8  I  513.6  +  1.08 

45  43  '  554-4  :-  i-'>8 
58().I  +  1. 10 


47 


48  38   630.8  +  1. 


360 
322 
284 
246 


246 
284 


360 
39S 
4j- 
474 
512 
550 
5S8 
626 
6&4 


+  7 
+  13 
+  23 


+  27 

+  28 

+  34 

+  32 

+  28 

+  36 

+  34 

+  37 

+  33 


5  3  107' -4  f   1. 13 

6  23  1 107. 3  +  1.13 

7  58  1150.3  +  1.13 
9  28  1190.9  +  I. 13 

10  38  1222.5  +  I. 13 

M  33  1247.2  +   I. 13 

12  48  12S1.1  f  1.13 

14  33  132S.4  ^-  1.13 

15  40  1301.3  ^  1. 1 3 
17  2S  1407.3  +  I. 13 
'8  53  1445-O  r  1.13 
2'  53  152O.7  +  1.13 

23  3  1558. 1  f  1.13 

24  30  1597-0  I  1.13 

25  48  1632.0  +  1.13 

26  58  1663.4  +  I. 13 
23  10  1O95.7  +  1.13 

29  43  1737-3  t-  1.13 

31  14  177S-I  I  I  13 

32  43  1817-8  ^  1.13 
34  18  1860.7 


•t  1. 13 
37   2   1933.5  +  I. 13 


702 
740 
778 
S22 
860 
897 
936 
974 


1050 
lo83 
1125 
II63 


1240 
1278 
1315 
1354 
1302 
1430 
14O8 
1544 
1587 
1O25 
1O63 


1739 


1S15 

■S53 
1891 

1955 


32 


+  37 

+  38 

+  30 

-)-  30 

+  27 


+  26 
+  24 


+  18 
+  >3 


+  I3 

+  31 

+  34 

+  26 

+  31 


+  17 

+  29 

+  28 

+  3" 

--  18 

+  43 

+  40 

■t  37 

••-  35 

+  31 


As  tliorci.s  !i  j,ar.  of  23  iiiiniitcs  in  tlic  ..hscrviithnis  nftcr  flic  liC'riuniii.r  w<.  1 


(liiriiio:  this  iiitcrviil,  110  ob.Horvntidiis  to  ci.mpjirc  witli  tlic>  correspt)!!!! 
011(1.     Tlu'  sum  of  tlio  14  ('(|iiiiti(>iis  after  the  hcoiui 


lavi' 


III"'  (incs  near 


the 


13.65  fl^  —309' 


liny'  IS, 
:+  22". 


Tlic  .siiiii  of  24  (•(|iiati.ms  most  iicfirl\  (■om..s|) lino-  to  tlicm  after  the  mi<Ml 

'26.45  (5£  =  675":    .-. /'>V-  +  2S".S. 


e  IS, 


The  remaiiiiii<i'  phases  lujar  the  eml  which   havi 
l)e},''iiiniii;i'  wouhl  "ive 


none  to  eorrcspoiid  to  them  near  th 


lU- 


f>£ 


=  +  27".4- 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


255 


1  think  this  result  sliould  l)e  rojei-tod,  iintl  thiit  we  shi.iild  tiikc,  iis  tlio  result   of 
the  olisci'Viitioii, 

df  =  +  24".!  ±  2". 

luUpSi-  (■/  1715,  '^fin  2,  ohii-iviil  hy  ///<■  Messrs.  I,\  lliui.  ,it  J\iris. 
Moon's  apparent  senii-ili.imetcr  at  hcKiiminj;     .      Mx)7  -5 
Moon's  apparent  sLMni-ilianiclcr  al  rnd     .            .      ion  ".2 
Sun's  a|iparem  scnii-iliaineler <)5'   -2 


La  Hirk,  the  father,  using  new  micrometer. 


La  llikK,  the  son,  using  Iniaxi;  on  screen. 




— 

( 

.11-1     t  n 

,     ( 

'orr.  to 

^oc.il  Mean 

I'aliular    V)\M.  of 

'"'^^"^•^''      lahntar     '-'" 

il  Mean 

I'aliular  Dis 

t.  ol" 

Observed     . 

'alinlar 

Time. 

Onlres. 

Distance. 

Dlsl. 

'iine. 

Centres. 

Distance. 

DiM. 

h      HI       s       \ 
20     1)     0 

t1j71.f1     —  1.151' 

1958.7-", 

-  12.9     20 

m     X 
9      0 

1971.6  -  1. 

5,1. 

1058-7-ni 

—  12.9 

>4      ') 

1313.0     -1.15 

1800.3 

-  13. f. 

14       6 

lSio.4  —  1 . 

15 

1800.3 

—  10. 1 

")    34 

!f'4')-5      -  1. 15 

1641.9 

-     7.f' 

'■<>    5f' 

1729.2-  1. 

15 

1 72 1.1 

-     S.I 

24    39 

I4i)f..S     -  1.15 

1433.5 

-  13-3 

19    21 

lf)53  5-1. 

15 

1641.0 

1 

-  1 1. 6 

31)       11 

1361.7     —  1 .  15 

1325.1 

-.lO-f. 

21     52 

1570-0-  1- 

15 

1562.7 

-17.2' 

33       • 

12(5.4     -  1.15 

r.'45-o 

+    0.5 

24    40 

1405-7  -  1- 

1; 

14S3.5 

—  12.2 

38    30 

uiijo,.^     —1.15 

10S7.6 

-     24 

27    33 

14<>).5  -  1. 

15 

1404.3 

-    5.2^ 

40    47 

1018. 0      -  1. 15 

1008.5 

-    9.5 

30    u 

l33':-3-  I. 

15 

1325-1 

-    5-7 

43    29 

930-2     -  1.15 

92<) .  2 

—  to.o 

33      1 

1246.8  -  I. 

1; 

1245.0         1 

-    0.9; 

4f)      0 

8f.f>.3     -I.  I? 

S50.0 

-  16.3 

35     10 

II78.8  -  1. 

If 

1166.7         1 

-  12. 1 

4.S    5'> 

7S».6     -  I. 15 

770.9 

-  13-7 

37    53 

1 100.6  -  1 

15 

10S7.6 

-  13.0 

51    40 

703.7      -  lit 

691.7           1 

-    12.0 

4"    5f' 

1013.4  -  I 

15 

1008.5 

-    4.9 

54    14 

631.1      —  1 . 1 3 

612.5 

-  18.6 

45    47 

S72.5  -  I 

15 

8  50.0 

-  22.5, 

50    4.S 

559. .J     -  1. 12 

533-3 

-  26.6 

40      7 

776.4  -  I 

"5 

770-9 

-    5-5i 

21       0     12 

467.0     —  t .  1 1 

454-1 

-  12.9 

52     14 

6S7.6  -  I 

l| 

691.7 

+    4. J 

3    16 

336.1      -  t.o6 

374.0 

-   11.2      21 

3    50 

371 .6  —  I 

05 

374.0 

+    3.3 

f.  24 

303.1       —  0  !>) 

293-7 

-     12.4 

6    33 

302.6  —  0 

87 

295  -  7 

-    6.9 

197.1      -0.5S 

208 . 9 

+  It. 3 

11     11 

209.9  -0 

.69 

216.7 

-t-    6.8: 

I 

I?     41 

201.6     +  0.50 

19"- 3 

-  11.3 

15    3; 

175.4  +0 

.02 

216.3 

+  41-4 

22     44 

276.3     +o.St 

296.  <' 

-'-  i'o.7 

22     10 

264.0  +  0 

.-s 

29O .  0 

+  32-0 

25    44 

344.7     +0.92 

375-3 

■t-  30.6 

25     51 

349.0  +  0 

.92 

375.4 

+  26.4 

3»    «5 

1    5t2.o     +  1.03 

533-0 

H    21.9 

28    50 

i    427.5  +" 

-00 

■     454-8 

+  27.3' 

35   ali 

596.7     4-  1.04 

613.2 

+  16.3 

32      0 

506.2  +  t 

.03 

534.1 

+  27.9 

V)      8 

61/).  3     +  '-"7 

692.5 

—     3.3 

35    24 

50f>-3  +  « 

.04 

613.4 

+  17. 1 

41    30 

^(to.2     +  t.o3 

771. 8 

+  1 1  . 6 

33    31 

680. 1  +  I 

.of> 

692.8 

+  12.7 

44    54 

852.5      4-  t  .09 

85  I.  2 

-     1-3 

41     14 

753-4  +  I 

.08 

772.1 

+  18.7 

■»7    34 

925.2      +11" 

930 -f) 

+     5-4 

44    32 

842.3   t    1 

.09 

851.5 

+    8.7 

5"    U 

101 1. 1      +  t.  to 

loto. 2 

—      (Ml 

47    3f' 

926.1    (- 

.  10 

030.9 

1    +    4.8 
I 

53    35 

108S.5     +  I .  to 

1089.7 

+      1.2 

50    24 

1002.1    ' 

.  10 

1010.3 

+     3.2 

56      f> 

I157-I    +1.11 

116(1.2 

4    12.1 

53    27 

1084.9  + 

.  10 

1089.6 

+    4-7 

1          5S    54 

1233.0    t-  1. 11 

1243.5 

+  If. 5 

5f>    47 

!lt74.f>  + 

.  II 

1169.0 

-    5.6 

22       ?     If. 

I.t<>4.9      )-  1.12 

1.407.0 

)      2.1 

50    34 

■  1251. t  4 

.  II 

1248.3 

-    2.8 

t 

S    5S 

1504.5      +  1.12 

1486.8 

-17-7     2 

2      2    44 

1336-8  + 

1 .  12 

1327.7 

j-     0-. 

11    5f> 

1566.4       +    I.I2 

1566.0 

-    0.4 

5    36 

14130  + 

t .  12 

1407.0 

i    -     6.0 

13    53 

1636.7        f-    1  .12 

1645. 1 

+     9.4 

8    45 

; 1408-7  + 

1    12 

1486.4 

-  12.3 

10    12 

1779.2        t-   1.12 

1803.8 

+  24 -f) 

14     12 

1645- I    t 

1 .  12 

1645- ' 

0.0 

22     17 

IS6I.6       +    I.I3 

1883. I 

(-  21 .6 

19    M 

1780.0  + 

1 .  12 

1803.8 

+  23-8 

25     31 

1947.8       +    1.13 

t96j.|-'i, 

+  14.7 

25     20 

1 1946.9  (• 

1.13 

'    11)62.4-0 

i    +«5.5 

^5^  RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 

'I'lio  1 6  iiioiisnres  of  the  fatlior,  t'ollovviii<>-  first  cfnitjict,  <>iv('  <U  —  -\-  i2".o 

His  iS  iiiojisiiros  invctMliiij.' lust  (■(iiitiict <'it=.+    ,S".8 

The  16  ol)servatiniis  oi'  the  sou  following'  lirst  coiitiiet  ('it  =:  -\-    j".i 

His  I S  (il)serviiti(iiis  preceding  hist  ('(iiitiiet (5*  r:  +    a". 2 

Ooiitiicts  ()l)serve(l  by  tlie  father ('^e  =  -\-  ia".i 

(.'oiitncts  ohservedhy  the  son '^V— 4-i4"6 

Tlie  coiitaets  nc.te.l   hy  tlie  two  observc^rs  agree  so  well   tliat  there  is  a  susi)i(i( 

of  their  not  being  independent.     The  eorresp,.in!fnee  between  the  .•onsi.l...-:.!,]..  <.,■••,. 

of  the  three   phases  i»reeeding   hist  contacts  miglit   gi 

respecting  tlie  ubser\atioiis  of  pliase.  Init  th 

tlirongh  the  observations 


111 


ecu  tne  consKlcrable  erroi.- 
rise  to 


similar  suspicion 


IIS  coiTespoiideiice  does  not  seem  to  extend 


(Jiving  tlie  coinbiiied  results  \ 


those  from  contacts,  we  shall  1 


roin   niejisiircs  of  phase   four  times  the  weight  of 


lave 


'5.  =  4-io".3±i' 


/u///>.\Y  flf  1715,  }r,iy  2.  ohanui  l<y  Cassim  „/  Marly. 


-■\%    5t'.7  ;   /  ^S" 


24"  cast  Irojii  (JK 


The  local  me.in  times  an-  lak.M.  wiilmui  rom-clH.n  from  ll.r  M.-n.ciis  „f  il,e  A.adcmv  f(,r  171;,  ,,„.  S3,  Sj   ai.i,lvinL. 


..  jin  22"  for  iMiiiation  of  timu 


al  Mean    Tal.iilai  1)1' 
ime.  ijff'nilr 


Ol.sci 
Disia 


■il      C 


Tal..  I)i,i. 


I.i>cal  Mean    Tahulai   Oisiaiici-    Ob 


Ti 


t)f  t"i 


lived      Co 


l)i 


rr.  to 
Tah.Disi. 


7  4"  IiJ7f'-4  -  1. 1? 'I' 

12     IS  1835.2  -    1.15 

17       f>  168S.:  -  1. 15 

22  57  1512. 1  -  1.15 

2()    2  I4lr).S  —  1.  15 

20    !<  1327-4  —1.15 

34  15  I175I  -  l"5 

3<)  44  ">i4-5  —  •  •  '5 

4;  2S  I  847. ()  -  I.  15 

52   2  ,  f)58.5  -  I.  14 

5')  4y  52f'-5  -1.13 


I3 


3fjf).f)  —  I  .()f) 
219.0 


i')5'J- 

i.?oo 

1484 
1405 
1326 
1 1 67 


f.92 
5.34 
375 

ai7 


•  >7- 

■35 
■47 

23 


34 


+    8 


21      14 
Ifi 


Ifiy.4 
180.2 


l!^  3S  214. 8 

^■4  53  34').n  +  o.()2il 

30  55  5o''i.S    \-  1.03 

37  54  f''}3.2  +  1.07 

43  42  849.8  +  i.oy 


55     38      1174.5 


f  I. 


13     38      I6fiu 


1512.7  +  1. 12 


h   I.  12 


177 
177 
21S 
376 


f>93 

852 

1 1 69 

I48f) 


If. 


8     1808.3  ^ 


24     28      I951. 


t   1 .  13 


45 
1S03 
Ii)f'2- 


+     8 


+     3 


+  28 


-27 

-  16 

-  5 

+  10  — (ij 


The  .systematic  errors  in  the  .'stimates  of  phases  are  .so  stronglv  marked  that  oiih 


I'oiTesiHdKU 


ng  ph 


lases  can  he  coniomei 


d.     Til 


tions,  the  siiiii  of  which  give  the  eipiatimi 

1  7.66  '*i^  —  -f  70'' 
The  obserxatioiis  ot   contact  almic  <>i\(' 


■ic  are  in  all  eight  pairs  of  such  ol 


)ser\a- 


+v 


''if  rr  +  I  2' 


Owing  to  the  extreme  irregularity  of  the  observations  of  phase,  T  think  tl 


of  contacts  are  entitled  to  as  iiiiicli  weight  as  tiie  wl 


le  pair 


phase.      The  result  of  these  observations  will  then  b( 


lole  eight  pairs  of  observations  of 


()* 


=  +  -S"  ±  4' 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON.  257 

J'Jclipse  of  the  Sun,  1715,  Mai/  2-3,  as  observed  in  England. 

Tills  eclipse  was  total  in  Hiij^land,  where  a  <^reat  niiinher  of  observations  were 
made,  tlu*  results  of  which  were  pnlilislu'd  in  the  I'liilosophirnI  Transaii'ions.  I'nfor- 
tunatelv,  in  the  lar<je  majority  of  cases  we  have  no  data  \vhat(!V(!r  for  judf^in};  of  tlie 
accuracv  with  wliich  the  time  was  (U?terinined,  and  the  observers  are  mostly  unknown 
as  astronomers.  The  wcdl-known  ol)servers  were  Flamstked,  IT.\i,m:y,  Foiixd,  and 
Cotes.  'I'he  latter  was  so  "oppressed  by  too  much  company"  that  lie  couhl  not 
observe  the  first  two  pliases;  it  may  therefore  be  ftsared  that  the  same  circumstances 
l)revent(Ml  an  exact  determination  of  clock-error.  II.vli.ev,  notwithstandin<r  his  scien- 
tific merits  in  some  directions,  seems  to  have  l)een  extremely  unskilled  in  every  l)ranch 
of  the  art  of  ])ractical  astronomy.  Porxo  made  many  observations,  but  then^  is  no 
way  of  ascertainin^r  how  well  his  time  was  (U'termined.  Fi.amsteeo  was  the  best  of 
the  observ(M-s,  but,  unfortunately,  his  ihita  for  clock-error  are  far  from  bein<i-  as  certain 
as  is  desirable,  'i'hese  uncertainties  are  especially  to  be  re<iretted,  because  the  ob- 
served times  of  be<ifinning  and  end  of  a  total  eclipse  are  not  subject  to  the  uncertain- 
ties which  affect  observations  of  the  other  pha.ses. 

There  was,  however,  one  class  of  determinations  maiU;  dnrinjr  this  eclipse  with 
an  accuracv  which  hardly  leaves  anything!-  to  be  desired,  and  for  wliich  we  are  probably 
iiidel)ted  to  IIam,i;v,  namely,  the  limits  of  the  path  of  totality.  We  have  here  the 
most  valuable  sinj^le  chitum  which  astronomy  ]»ossesses  for  determinin-;-  the  moticui  of 
the  nioon's  node;  it  is,  therefore,  vc^ry  surprisin<>-  that  it  should  have  i)assed  entirely 
luinoticeil  and  unused. 

In  discussinji:  this  eclipsi*,  we  shall  l)e<rin  with  the  En<j;lish  observations  of  the 
times  of  the  total  ])ha.ses,  rejectin;jr  those  of  the;  bef^nnniuf,''  and  end  as  uncertain  in 
comparison,      f^ast  of  all,  we  shall  discuss  the  results  of  the  shadow-limits. 

OhscrrnHoiis  of  Flamsteed. — Everytlnn<f  accessil)le  respectin<r  these  observations 
is  found  in  the  llisloiia  Coclfstis,  vol.  ii,  y.  551.  1  have  (f.xamined  the  orij-inal  manu- 
scripts at  (treenwich,  l)Ut  tinil  nothinu'  but  what  is  printed.  Some  li<rht  respectiu},'  the 
observations  may  perhaps  l)e  >ratlu!red  from  a  letter  of  Feamsteeh,  printed  by  lUn.v  in 
his  Aiamtit  of  the  Urr'.  John  Flainsfred,  pp.  315-316.  'I'he  followinj,'  are  the  essential 
observations,  giving  times  of  transit  over  nuu-al  quadrant,  and  iduises  of  eclipse: — 


Date. 

(Old  styliM 

rior 

k  Time. 

Truc.Vpp 
Tiiiit 

irenl 

Object. 

I7'5- 
Apr.      21 

1 1 

m 

I 

8 

24 
30 

J 

7 
31 
23 

3 

h     m 

s 

r  Hooiis. 
17  Bootis. 
K  Virginis. 
n  noolis. 

20 

II 

45 

20       5 

54 

Initiuin  Eel.  0. 

21 

M 

41 

21        q 

0 

Tdlalis  obscuratis. 

>7 

52 

13 

13 

I.UX  prima. 

>q 

1 

13 

31 

Venus  transit. 

23 

25 

32 

33     ig 

51 

Finis. 

2<< 

II 

II 

a8 

•  • 

3.1—    75  Ar.  2 


258 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Tho  (liserppaii)-  of  ten  socoiuls  in  tlie  clock-correction  for  bojrinninjr  I  cannot 
certainly  explain ;  it  exists  in  the  MS.,  and  may  I)e  a  correction  for  phase. 

'I'o  di'dncv  the  chu-k-correction.s  from  the  .star-transits,  mc  nui.st  know  tlio  (kiviation 
<»f  tile  (piadrant  from  the  meridian.  In  Kkikokh's  doctoral  dissertation,  Ik  Asrni- 
sioiiibiis  Iterfis  a  l-'lim.strnUo  (^mdiaiitis  Muralis  ope.  ohscrrniis,  lionn,  1854,  is  fonnd 
a  di.scnssion  uf  the  errors  of  the  (juadrant  in  1690,  in  which  the  following  valnes  of  m 
are  quoted  from  a  dissertation  l)y  Ahoklaxdek: — 

1690,  aetate  vernali  w  =  4- 26'.7 
1690,  aestate     .     .  -f-  aS'.g 

1699,  auctnmno     •  +35*-8 

1713,  mense  Jnnio  -f-69".4. 

These  are  the  corrections  to  reduce  the  observed  time  of  transit  of  an  equatorial 
•star  to  the  true  meridian.  Supposing  the  change  to  go  on,  the  correction  in  171 5 
would  have  been  about  +  -j^'.  Neglecting,  at  first,  the  p(.lar  deviation  from  the  meri- 
dian, we  have  the  following  (dock-corrections  from  the  star-transits: — 


May     7 


-  Bootis 
'/  Bootis 
«  Virg'nis 
<i  Bootis 
"  Hoolis 


("omnu 

I'd 

Clock. 

R.  A.  as 

com- 

M.an 

Time  of 

corr. 

Dec.  of 

putct 

. 

Transit 
True  M 

iver 

Deviation. 

Star.     1 

cr. 

, 

! 

//       m 

s 

/; 

m 

s 

m 

s 

1 

13     33 

■44 

10 

52 

57 

-   8 

10 

+ 

18  1 

41 

S 

II 

0 

20 

-   S 

II 

+ 

h;    ! 

57 

4f> 

IC 

55 

-   7 

33 

9 

U        2 

41 

21 

49 

-  8 

14 

+ 

20   ! 

2 

41 

2 

') 

-  <) 

"> 

-) 

20 

From  this  it  may  be  concluded  that  the  clock-correction  for  an  e.|uatorial  star 
on  May  2  at  i  i''.  i  would  have  ln-en 

Applying  AKtiiM-.vxoKK's  m  luigatively  . 


Clock-error  at  11''.  i _g 

Change  in  10  hours,  daily  rate  being  —  13" 


-  7-  42" 
-I"'  13" 


111     r  -^ 

53 


CI 


5" 


ock-correction  fin- middle  of  eclipse       _g 

Another  determination  of  the  error  of  the  quadrant  has  been  attenq)ted,  as 
follows:— On  1713,  Jmie  16-27,  the  clock-time  of  transit  of  the  su-.  over  tlie  true 
meridian,  as  derived  from  morning  and  afternoon  altitudes,  was  o''  7'"  11",  while  the 
transit  over  the  quadrant  occurred  at  o''  6'"  30",  showing  a  correction  of  -{-41".  Again, 
on  1718,  August  29-Sipteml)er  9,  the  true  transit  was  found  in  the  same  way  to  be 
wt  o*"  3"' 5"  dock-time,  while  the  transit  over  the  quadrant  was  marked  at  o''  i"'  54". 
We,  therefore,  have,  for  the  corre(!tion  to  the  (juadrant, 

I  713,  at  declination -f  23°:  c  rr-j-o"' 41". 
I  718,  at  declination  -f    5°:  c  =  -f  i'"  1 1*. 

The  mean  declination  of  the  three  northern  stars  observed  on  May  2  was -f  19", 
and  the  uncorrected  clock-correction  was  —  8"'  1 2".     The  correction  of  quadrant  inter- 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


259 


polated  to  this  declination  is  4S^  making-  for  the  trne  clock-error  — 9'"  o".  If  we  had 
taken  all  fonr  stars,  we  slioiild  have  had:  mean  clock-correction,  — S'"  i";  mean  decli- 
nation, -(-12';  correction  for  (piadrant,  59";  and  the  resnltinj;'  clock-correction  wonld 
still  he  —  9™  o".  ( !orrectin<T,  as  before,  for  rate,  tlu^  cf>rrection  for  the  time  of  the 
eclipse  is  —  9'"  5". 

The  correction  to  apparent  time  applied  by  Flaaimteki)  is  —  5'"  40",  and  the  ecpia- 
tion  of  time  is  —3'"  23",  so  that  the  correction  actnally  nsed  by  Fla.mstkkd,  of  the 
derivation  of  which  we  have  no  knowledtrc!,  is  —9'"  3".  \Ve  have,  then,  the  three  fol- 
lowin;^  rc^snlts  for  the  correction  to  Fi..vxisTEKJ>'s  clock  on  mean  time  at  the  moment 
of  total  eclipse: — 

Usinn-  Aii(iEi.ANnr.ii's  m —  9"  o". 

From  an  independent  discnssiim   ....     —  9'"  5". 

Fr.AMSTKKi)  actnally  nsed —  9'"  3"- 

The  value  of  Aroki.amikk's  ih  restinjf  on  an  "extrapolation",  and  its  applicability 
bein;,f  (luestion;ible,  not  much  weij^ht  can  be  jriviiu  to  the  first  result.  I  think,  there- 
fore, that  we  mayi)Ut  the  clock-correction  on  mean  time  at  —  9'"  4-,  and  that  the  error 
can  then  hardly  exceeil  3  oi-  4  seconds. 

Obserratioiis  hif  riAi-i-KV. — These  were  made  at  the  rooms  of  the  Uoyal  Society  in 
Crane  Court,  Fleet  .Street,  London.  A  re-reduction  of  his  altitudes  gives  results 
scarce! v  ditferinj^'  from  those  he  obtains.  The  correction  of  his  clock  on  mean  time 
is  — 3"'  38".      I  have  a.ssumed  his  position  to  be, 

A  rz    o'"  25"  west. 
The  longitude  may  be  some  seconds  in  error,  Init  it  would  be  a  useless  rertnement  to 
discuss  it  in  connection  with  such  oltservations. 

Ohsi-rrdtiniis  liif  I'or.ND. — Here  we  have  nothing  !)Ut  apparent  times,  and  can  do 
nothing   but  apply  —3'"  22',  the  etpiation   of  time,  to  his  results.     I'ouNu'.s  pctsition 


was, 


^  =  51°  34' 


A  zr    o»    8"  east. 
Eh'iiiriil-t  ilcriml  frmn    Tlicori/. — The    liusselian  elements   of   this   eclipse   are   as 
follows: — 


Greenwich  Mean  Times 

\^lllles  of  .V        ... 
Hourly  variation    . 
Values  ol  1' 
Hourly  variation    . 
LoK  sin  1/     .      .      .      . 
Radius  ol  penuniljra   . 
Radius  of  sliaduiv  . 


A     m 

K)      t2 

—  t  .5207(] 
+  0.56762 

+  <i.  31)727 

+  0. 12388 

9.42702 

0.53322 

0.01 21)!) 


//       ni 
20     24 

-o.S3<)3» 
0.56802 

+  0.54586 
o. 12367 
q. 42742 

"•53333 
0.01288 


2t 


36 


/; 
22 


jS 


"■■575-' 
u. 56824 
fo.6ijjoS 
o. 12327 
9.42781 

". 533-1' 
0.01280 


+  0.524:0 
0.56810 

+  0.S4170 
o. 12276 
9.4282 1 
0.53345 
0.U1276 


/(      III 
24       o 

+ 1 .  20^150 
0.56760 

+0.98870 
o.  12223 
9.42S60 

"•53343 
0.01268 


(  288  5r)  n.7    i  106  so  2C1.4       (24  'SO  40.8      3425052.4         051 


'i'he  notation  here  iiseil  is  thiit  of  §  7.     The  radii  of  the  penmnbra  anil  shad'tw 
are  those  which  (■("•n^sDond  to  the  fundamental  }>lane  of  reference,  passing  through  the 


26o 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


centre  of  tlio  earth  ixTpeiulicular  to  tlie  axis  of  tlie  sliadow.     Tlie  value  of  n  is  tliat  of 
//'  (■oiTospoiKliii'r  to  tlio  meridian  of  Greenwich. 

From  these  (hita  we  obtain   tiie  fonowinfr  observed  and   computed  local  mean 
times: — 


Place. 

Observer. 

Total   Phase. 
Beginning    . 

Local  .Mean 
Time  ol)s. 

h     m     s 

21      5    37 

Local  Mean 
Time  conip. 

m    s 
f)     34 

Coireciion. 

Greenwich    . 

Flanistted    . 

1 

-  57 

End   .      .      . 

21        S     48 

9     32 

-  44 

London  . 

Halley    .     . 

Beginning   . 

2'      5    39 

6       I 

—    22 

End   .      .      . 

21      t)      2 

<j     12 

—    10 

Wansicad     . 

Pound     . 

Beginning    . 

21      f)      fl 

f)    48 

-   42 

End   .      .      . 

21      926 

9     52 

-    26 

At  the  general  mean  of  these  times,  and  for  the  position  of  Greenwich,  we  have, 
very  nearly,  for  the  (■hiin«;(^  in  the  time  of  the  ithase  proiiuced  bv  a  chanoe  of  i"  in 
the  Uinyitude,  A,  and  the  liititude,  fJ,  of  the  moon, 

Befjimiing-  of  totality  ;  (5/,  =  —  2. 13  (^ A  -f  1.52  f5/y 
End  of  totality  ;  6t.,  =  —  2  04  <SX  —  2.04  S/J. 

To  make  use  of  tiiese  quantities,  we  must  express  the  correction  of  the  moon's  true 
longitu(h!  and  latitude  in  terms  of  that  of  lier  mean  longitude  and  hmgitude  of  the 
node      We  find,  from  tlie  ftrmuhe  already  given, 

'^A  —       1. 14  i)a  ^ 

Sfi  =  —  o.  100  f5f  -f  0.0S8  <50, 

which  e.xpressions  iire  to  be  suljstituted  in  the  preceding  ecpiations  of  condition. 

\Ve  have  now  to  coinl)iiie  the  observation.s.  Their  remarkable  di.sconlance  ren- 
ders the  final  result  greatly  dependent  on  the  relative  weiglits  a.ssigned,  and  these  jire 
necessarily  a  matter  of  Judgment.  The  most  widely  discordant  ones  are  those  which 
we  should  suppose,  from  the  data  before  us,  to  have  been  the  liest,  namd  ,  IIali.kv's 
and  Fi.AM.sTKLo'.s.  Altogether,  I  think,  the  most  probable  result  will  l)e  olitained  bv 
giving  1 1. \  I. LEV  and  Toind  the  weight  1,  and  I-'lamsi  i;ki.  weight  2.  At  the  same  time, 
I  confess,  that  my  judgment  may  lie  iiiHueiiced  in  this  decision  1)\-  the  entirely  improl)- 
alile  corn'ction  to  the  tabular  times  which  is  indicated  b\-  Fi.v.Msi  ill's  ol)servations, 
and  that  Itut  for  this  1  might  assign  a  greater  relative  weight  to  the  latter.  <  >u  the 
other  hand,  were  it  not  for  the  e(pially  yreat  deviation  of  IIai.i.kv's  obseivations  from 
prolial»ility  in  the  opposite  direction,  I  might  assign  him  a  greater  weight  than  i'oLXD, 
and  the  result  would  then  l)e  luit  little  altered..  I  shall,  therefore,  adhere  to  the  above 
weights.     This  combination  will  give, 

.Aleaii  correction  to  beginning  .     .     .  'V,  —  — 44' 

.Mean  correction  to  end      ....  .     'V^  :r  —  31". 

Hy  substituting  the  values  of  'V,  -^A,  etc.,  in  the  etpwitioiis  of  coiulition,  they  become, 

2.58  '^4  —  2.0  f^A  —  o.  1 34  'W  —  44 
1.76  <5*  —  2.0 '5Zy-|- 0.1  79  (5  >  —  31. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


261 


Puttinif  fSL,  the  correction  to  the  .sun's  lonjiitude,  ecjuiil  to  zero,  wo  derive  from  those 
equations 

<U  =  +  i6".2±2".5 
SO  =  —  20". 

Tlie  correction  to  0  will  lt(^  ol)taino(l  so  nincli  more  accurately  from  other  ol)ser- 
vation.s  that  we  need  not  consider  it  here. 


§  15. 

DISCUSSION  OF  DEVIATIONS  IN  THK   MOON'S  MKAN  MOTION  AS  INDICATED  BY 

THE  I'UECEDINO  OBSERVATIONS. 

We  now  employ  the  precedinfjf  results  for  the  study  of  the  principal  problem  in 
view  as  the  ol>jcct  of  these  researches.  If  we  supimse  no  deviation  in  the  mean  motion 
of  tlie  mo(m  except  that  which  is  due  t(»  the  {fravitation  of  other  boflies  of  our  .system, 
this  mcfan  motion  woidd  l)c  constant  with  the  exception  of  a  secuhir  acceleration,  the 
amount  of  wiiich  has  lu-cn  accurately  lixcd  liy  theory.  Ft  is,  iiowevcr,  well  known  that 
the  secular  acceleratiftn  ^^ivcn  l»v  oljscrvation  is  not  the  .same  as  that  deduced  from 
theorv,  and  astronomers  have  jicnerally  been  ai'reed  that  the  apparent  dift'erence  may 
lie  due  to  a  retardation  of  the  earth's  axial  rotation.  Thus,  the  apparent  sccidar  accel- 
eration will  be  made  up  of  two  parts, — the  one  a  real  acceleration;  the  other  an  a|)parent 
one,  due  to  the  chan<ye  in  onr  measure  of  time. 

But  when  we  studv  the  pnthlem  more  clos(v'ly,  we  shall  ttnd  that  the  hypothesis 
of  a  constant  tidal  retardation  fails  to  accaunt  for  the  observeil  mean  moti<ni  of  the 
moon,  and  that  we  nuist  eitiier  suppose  this  retardation  varial)le,  sometimes  even 
becoming  an  acceleration,  or  we  iinist  suppose  the  mean  motion  of  the  moon  sul)ject  to 
changes  which  have  not  yet  been  accounteil  for.  Let  as  now  impure  what  deviations 
of  the  moon's  mean  motitni  remain  unaccounted  for.  For  this  pnr|)osc,  we  collect  from 
the  two  preceding  sections  the  following  .system  of  residual  correctimis,  ot)taine(l  from 
the  observations  of  edijKses  and  occultations  made  since  the  invention  of  the  telescope. 
We  begin  with  iiulividual  results  from  each  eclipse  and  from  groups  of  occultations.  It 
mav  once  more  l)e  remarke(l  that  the  prol)al)le  ernu's  here  a.ssigned  are,  for  the  most 
part,  mere  estimates,  foundeil  on  a  consideration  of  all  the  attendant  circunistanc(!S. 
Some  such  estimate  is  absolntelv  necessary  for  the  suhse<|Uent  combination  of  the 
(»bservations;  and,  as  there  are  no  data  for  the  rigorous  computation  of  probable  errors, 
we  are  necessarily  left  in  part  to  the  exen-i.se  of  our  judgment. 

Individual  Corrections  to  tin   Mean  Loiiijititdr  of  llic  Moan  in  Hansen's  Tables,  a-itli    the 

Soiireis  irlniicc  dcrired. 


1621.4, '5-  =4-  7«"   i-  14" 


1630.4 

+  35 

1 

-5 

•633-3 

+  S3 

:L 

<3 

•63.S-7 

+  57 

i- 

9 

1639.4 

+  34 

-1 

1  1 

1639,4 

+  23 

± 

9 

1639.4 

+  27 

± 

5 

(lAssENUi'.s,  li('friniiiii(;  and  t'lid  of  eclipse. 
(lASSioNurw,  iit'^iuiiiiit;  lit  fcliii.se. 
OASSKNurs,  ci'lipsi'©,  phnses. 
Bi'i.LiAi.nis  anil  (iAssi;ni)i;s,  13  iMciiltatinns. 

El'lip.si'0,  It.V  (lASCOUiMO. 

Ei'lipst'©,  li.v  (jAsskm)Is. 
Eclipsf  0,  bj  IIoRUux. 


262 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


1639.4,  lU 

=  -27" 

+  (T)" 

1645.2 

■t-3-J 

±  10 

1645.6 

+  5' 

±  8 

^<^5^-3 

+  38 

+  lO 

1654.6 

+  3> 

±     8 

1 661.2 

+  37 

i  6 

16C2.0 

+  38 

+  5 

1666.5 

+  25 

±  10 

'673-9 

+  39 

+  4 

1676.4 

+  23 

±  6 

1 680,0 

+  3' 

+  5 

1680.0 

+  29.4 

^+  1.0 

1684.5 

+  24 

+  4 

.6S4.5 

■^-3^ 

±  2 

1699.7 

+  24-f 

i  ±  2.0 

1706.4 

+  24- 

:l:   2.0 

'7 '2-5 

+  14.8  i  0.6 

'7 '5-3 

+  16.. 

'..i:      2.5 

■715-3 

+  8 

+   4 

'7>5-3 

-f  10. 

?+  '-S 

1728.5 

+  7-3+  '-5 

E(!li|tKe0,  by  Ukvelius. 

4  |)ll)l^i(•H  of  u(tciillali(>nH,  by  Hkvklium. 

E(li|im'0,  by  JlKVELlus. 

Kiii|i.sc' 0,  by  IIKVKLIU8. 

K(!lipst'  0,  liy  VValtekius. 

Kcbpst'  0,  by  IlEVEMua. 

OcTiiltatioiis,  by  Hevemus. 

E(;li|).si'  0,  by  HkVKMUS. 

Occ.iiltiitiDiist,  by  Hevemus. 

Kclip-st'  0,  by  Flamstekd. 

Oiciiltatioiis,  by  Hevki.U's. 

Occiiltatioiis  by  Flamsieei)  ami  the  PaiLs  a.strouoiiierH. 

Kclipsc  0,  by  Flamsteeo. 

lM!lip.s('0,  by  La  Hike. 

Fclips('0,  by  La  Hike. 

Ei'lip.sc0.  by  La  lIlRB. 

(Jciuiltiitimi.s,  by  tlio  Paris  astroiioiriiTs, 

FHip,sf0,  by  Fi-AMSTEEU,  IIalley,  and  Pound, 

Kt'lipst'0,  by  Cassim,  at  Marly. 

Ki;lips»'  0,  by  the  La  Uikes,  at  ParJH. 

Oc'caltatioiiN,  by  Delisle,  etc. 

The  (lisconl.ances  among  the  ohler  results  tire,  on  the  wlioh',  not  greater  than 
what  we  .should  I'.xiiiK't  from  the  probable  errors  assigned,  i'.\c('|it  in  the  case  of  the 
ellipse  of  1639.  In  faet,  if  we  suppose  tiu'  error  of  the  tal)Ies  to  dimini.sh  uniformly 
from  60",  in  1620,  to  30",  in  16S0,  tiie  deviation  of  the  result  will  in  no  case  e.xceed 
t.5  X  f''^'  probable  error  assigned,  except  in  the  civse  of  the  observations  of  the  ecdip.se 
of  1O39,  by  (iAssKNDis  and  IIorkox,  where  the  deviations  are,  respectivelv,  3.0  and 
4.6  X  prol»al)lc  error.  'The  ([Ui'stion  whether  the  olhservations  are  (u-  are  not  to  be 
taxed  with  tliis  apparent  error  cannot  now  be  settled. 

'I'd  investigate  the  (piestions  now  under  con.sideration,  we  nmst  linve  the  correc- 
tion to  II.usskn's  Tables  given  by  observations  from  1750  to  the  ])resent  time.  From 
the  comparisons  piiltlislicil  l»y  11.\nskn  himself  in  the  Mimthhi  Xaticr.s  of  tlii'  Itoi/al 
Ashniiiiiiiiiiil  Sniicli/,  it  would  appear  that  the  correction  from  1750  to  1S50,  inclusive, 
is  very  nearly  zero.  The  coiu'se  of  the  ino<»n  since  1S50  has  been  investigated  in  Part 
III  of  the  J'dfxr.s  piililislii'd  hi/  Hir  ('niiii)ii.ssinii  011  the  TriiHnil  of  Voiks,  from  wliicdi  it 
apjicars  that,  at  the  epoch  1S75.0,  the  meridian  ob.servatiiuis  at  (Jreenwich  and  Wash- 
ington indicate  a  correction  to  the  moon's  mean  htngitude  of  — 9". 7.  Uut  the  occul- 
tatious  about  the  same  time  give  a  correction  nearly  two  seconds  less,  so  that  we  nuiy 
consider  the  correction  at  this  epoch  to  lie  — 8". 

The  iirst  (piestion  to  l)e  considered  is  how  nearly  the  ob.servati(Uis  can  be  repre- 
sented by  thenry  without  any  em|tirical  correction.  It  is  well  kiu)wn  that  Hansen  intro- 
duced into  his  tai)les  a  term  depending  <>n  the  argument  8  times  the  mean  motion  of 
Venus  minus  13  times  the  mean  motion  of  the  earth,  which  is  to  be  regarded  as  (;mpiri- 
cal,  .since  it  has  never  been  satisfactorily  shown  to  have  any  theoretical  existence.     We 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


263 


must  thcroforo  rpmove  tliis  term  from  the  tlicoi y  to  lie  compiirfil  witli  oliscivjitioii. 
'riic  s(!<'iiliir  iU'cclcnitioii  i.s,  however,  to  be  left  iirljitriiry,  l)eciiiise  it  ilcjieiuls  in  |iiirt 
on  the  unknown  ti(hil  retimhition  of  the  eiirth's  rotiition. 

For  convenience  in  solving"'  tlie  ('([niitions,  we  slmll  nTiiphiciilly  inter|M.hite  the 
indivi(hml  corrections  to  the  moon's  mean  h>n;iitM(h'  jnst  coMected,  so  as  to  </\\{'  the 
vahie  of  that  correction  for  intervals  of  a  (|U«rter  of  a  centnrv.  'I'he  vahies  of  the  cor- 
rections to  Hanmkn's  Tables  thus  interpolated,  of  IIaxskn'.s  doubtful  term,  and  of  the 
reaultiuff  correction  to  a  piu-e  theory,  an-  as  follows;  l'.^  re|iresentinff  the  donbtfid 
term  and  6t'  the  correction  t(»  pure  theory: — 

1625,  .5*  =  +50"  ±13";     r,rz-  17"..;    .>!*'  = +33" 


1650 

+  39 

± 

5 

— 

21.4 

+  18 

'675 

+  32 

± 

— 

16.8 

+  ■5 

1700 

+ 

21 

± 

— 

5-2 

+  16 

1725 

+ 

7 

± 

+ 

8.6 

+  16 

1750 

0 

rt 

+ 

18.9 

+  19 

1775 

0 

± 

+ 

21.2 

+  21 

1800 

0 

± 

+ 

14.7 

+  •5 

1825 

0 

± 

+ 

2.1 

+  2 

1850 

0 

± 

— 

1 1.4 

—  I  I 

•875 

— 

8 

± 

— 

20.1 

-28 

It  is  clear,  without  comimtation,  that  these  residuals  cannot  be  represented  bv 
corrections  to  the  epoch,  mean  motion,  and  secular  acceleration.  The  onlv  secular 
accelerati<v.i  we  can  obtain  is  an  api)roxiniation  to  a  mean  value,  which  mav  have 
dirt'erent  values  acc(»rdin<^  to  the  mode  of  usin<>'  the  data,  because  the  mean  in  (piestion 
does  not  admit  of  precise  definition.  The  deviation  during  recent  years  is  such  that 
the  secular  acceleration  will  come  out  smaller  the  greater  the  weight  we  assign  to  the 
modern  observations.  T(»  (d)tain  the  best  residt  from  the  ancienr  and  mo(leni  obser- 
vations combined,  it  seems  advi.sable  to  assign  a  minimum  proliable  error  of  4"  or  5" 
to  each  residual  of  the  modern  observations. 

The  equations  of  condition  given  by  the  am-ient  and  modern  corrections  are  as 
follow.  In  the.se  ecpuitions  we  have  i)ut  <U  for  the  correction  to  the  moon's  mean  lon- 
gitude in  seconds  in  1700,  and  I'^ii  for  the  correction  of  the  centennial  mean  motion  at 
the  same  epoch,  while  »5.v  is  the  correction  to  IIanskn'.s  .secular  acceleration.  'I'he  first 
four  e(puitions  are  those  given  by  Ptolemy's  lunar  eclipses,  p.  44,  while  the  next 
three  are  tho.se  from  the  Arabian  ol)servations,  p.  5.^.  To  obtain  a  mon-  convenient 
treatment  of  the  eciuations,  the  residuals  of  the  ancient  ol)servations  are  ex])res,scd  in 
minutes  of  arc  instead  of  seconds.  The  etpiations  exprcs.sed  in  seconds  may  be  con- 
sidered as  divided  by  60  throughout,  and  the  weights  as  nndtiplied  by  3600.  The  unit 
of  weight  is  suj)j)osed  to  correspond  to  a  j)robable  error  of  about  6  units 


364 


RESEAF^HES  ON  THE  MOTION  OF  THE  MOON. 


Kqidilioiis  of  ('i)iiilitioii  for  the  M<,<,i,\-<  Mm,,  M „/!„„,  etc. 


hiifc 


—  687; 

—  I  Sq  ; 


0.01  7  Af  _  0.40  'hi  +  9.55  I'i.s  rz  —  I  (  ;      \Vt.  — 


.or7 
.017 
.017 

.017 


927;       .017 
986;    0017 


1625; 
1650; 

1675; 
1700; 

1750; 

1775; 
1800; 
1H25; 
1850; 

'«75; 


1. 00 
1. 00 
1. 00 
I  00 

I. GO 
I. GO 
I  GG 
I  00 
LOG 
I.GG 
LOG 


-0-35 

—  o  ;,  I 

—  0.26 

—  0.14 

—  o.  1 3 

—  0.1 2 

-075 

—  0.5G 

—  0.25 

O.OG 

+  0.25 

0.50 

0-75 

I.GG 

1-25 
I.5G 

1-75 


+  728 

+  5  95 
+  4. 1  I 

+  1.20 
+  G.09 
+  G.84 

+  0.56 
+  0.25 
+  0.06 

GOO 
+  0.06 
+  0.25 
+  0.56 
-f-  1. 00 

+  1.56 
+  2.25 
+  3.06 


-27 

—  20 

—  lO 

-  4.4 

—  I.I 

—  4-X 

+  33 
18 

'5 
16 
16 
19 

21 

15 
+  2 

—  I  I 

—  28 


3  • 

/•n-f  16' 

2 

-    7 

4 

-    4 

3 

—    6 

8 

-    2.4 

16 

+    0.3 

30 

-    3.« 

I 

+    6". 

1 

-    6.9 

2 

-    7-4 

2 

-    3-6 

2 

-    0.3 

2 

+    '3,4 

3 

+  '2.5 

2 

+  III 

2 

+    3.0 

2 

-    4-6 

2 

-15.8 

If  will  1)(.  in.ticeil  thiit  tlu-  (-(.iTectioiis  frnni  the  Aniliiim  ..l.s..|Viiti(.iis  iinpldyiMl  in 
the  e<,njiti..ns  iiiv  a  littlti  (liHbrent  from  thoso  -iv.-ii  <>ii  p.  54.  '|"lns  anse.s  tn.in  tfic  fact 
that  .'.|iial  wcijilit  was  ^ivcii  to  all  the  ccliiisc*  in  funiiiii;.-  these  e(|Matioiis.  TIk-  final 
result  is  snl)staiitially  the  .sanut  on  either  system. 

Treatin^r  ilie  above  equations  by  the  method  ..f  leasi  squares,  we  have  the  nor- 
njiils : — 

20.02  (Sf  +  I  2.07  '5»  -f-  20.62  Ss  —  4-  I  74.0 
12.07  +20.60  —  9.66  zz-\-  15.2 
20.62       —    9.66       +657.1  =—1687.0 

The  solution  of  whieh  gives : — 

c5fr.+  I9".57^ 

Sh-=—\ 2".3 1  y  Ei)och,  I  700. 

'5.s=-    3".36> 

If  we  transfer  the  e[)och  to  1800,  the  corrections  will  be: — 

''>*  =+    3".90^ 

(Sh  =  —  1 9".03  [•  Epoch,  1800. 

6s  =-    3".36^ 

If  we  sulwtituto  these  values  of  the  unknown  (|uantities  in  the  equations  of  con- 
dition, we  shall  have  the  residuals  ftjllowinj,--  the  e(|uations.  We  .see  that  in  the  case 
of  the  modern  observations  the  residuals  are  of  an  entirely  inadini.s.sible  niaf,niitudo; 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


26s 


it  \H  tlicrffurc  ocrtiiin  tliat  tin-  cxistiii;.'-  tlicurv  will  not  roprcsciit  ohsorvntions  with 
any  vmIiic  wliatcvcr  of  tlic  secular  accclfratimi.  Still,  the  comM'tioii  which  we  havo 
(lediiced  for  the  secular  acceleration  is  clearly  imlicated  hy  the  conildnation  of  all  thu 
obHervations.      1Ia\si;n',s  adopted  value  Ix-iu}--  12".  17,  wo  ure  lod  to  tho  vuluo 

s  =  8".8 

(IS  that  which,  on  the  whole,  hcHt  satisfioH  the  obHorvati(»ns  wliicli  w(!  have  discussed. 

Uespectinjr  the  cause  of  the  outstandinf^  deviations,  wo  may  make  two  hvpo- 
the.se.s : — 

(1)  That  these  deviations  are  only  apparent  ones,  arisin*,'  from  ine(|Ualities  in  the 
axial  rotation  of  the  earth.  The  deviation  of  tlu*  observed  secular  acceleration  from 
tho  theoretical  value  6".i,S  has  lonjr  boon  attributed  to  a  retardation  of  tho  earthV 
rotation,  and  liy  supposing-  tliis  retardation  to  be  it.solf  a  varialtle  (pnintitv,  and  indeed 
sometimes  to  chauf-c  into  an  acceleration,  we  may  completely  account  for  the  observed 
deviations. 

(2)  We  may  suppo.se  the  deviations  to  ari.se  from  one  or  more  incMiualitioH  of  long 
]ieriod  in  tla^  actual  mean  motion  of  the  moon. 

l.et  us  consider  the.se  two  hypotheses  in  order.  Wa  have  first  to  see  what  result.s 
foUow,  if  we  suppose  the  theory  of  jrravitation  to  correitly  account  for  all  real  clian;fes 
in  tho  mean  motion  of  the  moon,  and  attribute  the  observed  deviations  to  chan>,'es  in 
the  earth's  axial  rotation,  or  the  len;>th  of  the  mean  day.  To  Hud  what  the.so  devia- 
tions really  are,  we  inu.st  take  out  tlicf  eUect  of  IIanskn's  increase  of  the  secular 
acceleration  as  well  as  the  empirical  term  due  to  the  action  of  N'enus  from  the  thoorv 
to  be  compared.  The  latter  has  been  taken  out  wherever  ne< cssary  in  the  preceding 
eshil)it  of  the  corrections  to  the  nuton'.s  moan  lon<ritude,  and  it  now  remains  to  consider 
the  former. 

The  sidereal  acceleration  adopted  in   Hanskn's  tables  is  la'.i.S  7'" 

While   Dki.ai  NAV  has  found  from  theory     .     .          .     .  6".iS  7''' 

So  tliar  tile  excess  of  IIanskn'.s  tables  is 4-    6".oo  T". 

If  we  apply  ihis  comM-tion  to  the  tabular  residuals,  we  shall  have  the  results  of 
the  hypothetical  deviations  from  a  certain  uniform  measure  of  time.  '^Fliis  measure 
beinj;  arl)itrary.  we  shall  take  it  .so  that  flie  observed  and  the  assumed  measures  .shall 
ajii-ee  in  1-50  and  1850.  This  will  be  elVected  by  correcting  the  residuals  by  the 
quantity 

-29".5  4- 18".o7'  +  6"o  7'-, 

r  being  (counted  in  centuries  from  i  700.  .applying  this  correction  to  the  fundamental 
residuals,  we  have  the  series  of  outstanding-  correlations  to  pure  tlieory  given  in  tho 
secrond  colunm  of  the  following  tal)le,  while,  in  the  third  coluuni,  these  residuals  are 
converted  into  seconds  of  time.     The  si^iiiticance  of  the  numbers  in  (piestion  is  this: — 

// wi;  si(i)jii)sr  flic  niic)tl(i(  flirnri/  of  tin-  moon's  motion  to  be  iwrfcrt.  uud  the  observed 
deviations  from  tlieinji  to  be  dm  to  ineniuilifies  in  the  earth's  axial  rotation,  then  the  last 


a66 


RKSEARCIIES  ON  THE  MOTION  OF  THE  MOON. 


rohiiinioj  lliis  tiihir  slmirs  fhr  iiihoioiI  in  (imr  hi/ wliicit  tlir  rinili  is  i)i  dilrttnrr  of  an  (i.ssiimril 
unijonnlii  rcroli>iiii/  ciirlli.  Tlifxr  niniilnrs  mnsf  tlirrrf'orr  hr  siihfidiird  from  the  tiiiws  indi- 
cated by  asliiinoiniciil  ohsi-rrations  in  order  to  ndmr  tlnm  to  it  idiijiiriu  mvasnrr  of  time. 


-M7; 

''*  =  +  . 

3X'.6,  J 

ilz=—  70" 

-381 

+  " 

9.9 

-  18 

—  1 89 

+ 

9.6 

-  17 

+  '34 

+ 

3-5 

—  6 

846 

— 

0.2 

0 

926 

+ 

2.1 

-  4 

986 

— 

1-3 

+  2 

1625 

— 

6".6 

+  12* 

1650 

— 

19.0 

+  35 

'675 

— 

18.6 

+  34 

1700 

— 

'3-5 

+  25 

'725 

— 

8.6 

+  16 

1750 

0.0 

0 

1775 

+ 

8.4 

-  15 

1800 

9-5 

-17 

1825 

+ 

4-4 

-  8 

1850 

0.0 

0 

'875 

— 

7.6 

+  14 

These  corrections  are  so  mimitc  tliut  tlicir  iiidcpendont  detection  by  existing 
ol)sprviitions  is  hiirelv  |)ossil)l('.  'Plic  most  proniisiiijf  moans  of  detection  is  atFoi'tled 
by  the  eclipses  of  tlu!  first  siitcllite  of  Jupiter,  wiiicii  lia\e  been  obscirved  since  1670. 
Next  in  order  coino  meridian  ttbservationK  of  Venus  (hirin<;  several  months  on  each 
side  of  her  superi(U'  conjunction,  the  discussion  of  which  would  be  extremelj'  lal)orious, 
and  would  involve  a  complete  re-e\aminatioii  of  tlu^  theorv  of  the  motii>n  of  Venns. 
Transits  of  .Mercury  also  atl'ord  some  hope,  but,  unfortunately,  |[.\i-i,Kv's  excellent 
observation  of  the  transit  of  1678  is  vitiated  bv  some  defect  in  his  ch»ck-error,  which 
cannot  be  investif^ated  for  want  of  data. 

If  the  hypothesis  in  ([iiestion  is  correct,  tins  pr(d)lem  of  predicting;  the  nnxm'B 
motion  with  accuracy  throujih  lonj;-  intervals  of  linu'  nnist  be  re;.''arde(l  as  ho|ieless, 
since  it  cannot  be  expected  that  variations  in  the  earth's  axial  rotation  will  conform  to 
any  determinable  law.  Suc(^ess  in  tracing;'  the  deviatii.ns  in  (piestion  to  the  nuHiu  itself 
and  to  the  theory  of  firavitation  is  therefore  a  consnuunation  to  be  hoped  for. 

I'assiujf  now  to  the  second  hypothesis,  a  <ilance  at  the  residuals  of  the  e(puiti(Mis 
of  condition  on  paye  263  shows  that  the  modern  ob.servations  may  be  very  nearly 
n^presented  by  a  term  having  a  period  of  between  250  and  300  years,  iict  ns  then 
intjuire  how  {^ood  this  repnssentation  can  be  made  if  we  sup|>ose  an  empirical  correc- 
tion to  Hanskn's  first  term  dependin^;■  on  the  action  of  Venus,  the  ptniod  of  which 
is  273  ^ears.  In  this  inquiry,  we  contine  ourselves  to  the  modern  observations;  and 
we  mn.st  introduce,  in  addition  to  the  term  sought,  new  corrections  to  the  nu)on'8 
ch  and  menu  motion.     Let  ns 


ejiocl 


J)Ut 

A  =  iS  F-i6i'- 


9; 


RKSF.ARCIIE.S  ON  TIIK  MOTION  OF  TIIF  MOON. 


J67 


riM-iiiy  tlic  iiK^iiii  Iniij-itinlc  (if  V(;mis,  /■;  tliiit  i.f  tlic  caitli,  and  //  tin-  mean  anunialv 
ttf  tiie  moon.     Tlio  rcwiilual  »oiii'('tiHn.s  will  then  lir  of  tin-  form 

At  -\-  Ti^n  -\-  ./•  .sin  J  -|_  y  (.,,s  ^1. 
Cctiintinjf  T'\\\  coiiturios  from  i3oo,  tlio  o(iuution.s  of  condition  will  bo: — 


rfe_  1.75  ,S„_ 0.73x4- 0.68;/  =  4-    6".i         \Vt.=:    ^ 

(5f—  1.50       —0.24  4-0.96  =r—    6". 9  I 

4-0.33  4-0.95  =-    7".4  j 

4-0.79  4-0.62  =—    3".6  5 

4-  1. 00  —0.09  =.—   o".3  3 

4.o,,SS  —0.47  =4-    6".4  4 

4-0.4.S  -0.87  =4-i2".5  4 

—  0.07  —  1. 00  1=4- 1 1  ".I  4 

—  060  —080  — -f    3".o  4 

—  0.94  —0.34  =:—    4".6  8 

—  0.97  4-0.22  =:— I5".8  10 


^e—  1.25 
''>■«  —  1. 00 
«5f  —  0.75 

^E  —  0.50 
<U  —  0.25 
<^f         0.00 

(5f  4-0.25 
&£  4-  0.50 

'5*  4-0.75 


The  unit  of  W(!i<'lit  i.s  suppo.scd  to  correspond  to  a  prohahlo  error  of  about  ±  2' 
Tlio  treatment  by  least  .s(|uare.><  leads  to  tin   normals: — 

48.500 '5*  —    6.375  A«_    6.465./—    3.660//  =  —  i22".55 

—  6.375       4-27.401       -21.13S     —    9.975    ——    89".26 
-6.465       -21138       4-28946     4-    3.107    =4-i96".i7 

—  3.660       —    9.975       4-    3.107     4-19.492    =  —  182". 72. 

The  solution  of  tho.se  o(iuatioiis  irives: — 

'^f  =  — 


'U  =  -    5".o4) 

'5,<  =  -io".i4r'l'"''''  '^°°- 


XZZ  — 

0 

.09 

y  =  - 

>5' 

■49. 

The  oiitstatidinj^-  residuals 

iire:  — 

1625 

+  3".9 

1775 

4- 1".6 

50 

-  2".2 

1800 

4-  o".6 

75 

~o".3 

25 

-  •"•9 

1700 

4-  i".o 

50 

4-0".  2 

25 

-  o".8 

'875 

4-o".2. 

SO 

-  o".8 

The  empirical  iiltoratiou  in  (luestioii,  therefore,  ro]»roseut8  the  observations  quite  satis- 
factorily. 

The  additional  dimiinition  of  10"  per  century  in  the  mean  motion  of  the  moon 
at  the  ))re.sent  time  will  nece.ssitate  a  farther  diminution  of  o".5  in  the  value  of  the 
secular  acceleration  in  order  that  the  ancient  ob.scrvations  mav  still  be  well  repre.sented. 
'I'his  will  leave  the  moon's  lonj^itudo  unaltered  by  the  last  correction  at  the  ei)oeh  —  250. 


268 


RESEARCHES  ON    HIE  MOTION  OF  THE  MOON. 


To  rcprcMeiit  the  Araliinn  cbsL'i'ViVtion.s  without  Jiiiy  iiu'ini  rcsidiuil,  tlu*  diininntion 
.xhoiild  he  about  .?",  so  that  the  observed  secidar  acc«'lerati<iii  woidd  lie  riMluced  t'ldlv 
to  its  thctiretical  vabie,  h-avinj;  no  tiihd  retardation  whatever.  'J'he  best  mean  repre- 
sentation of  the  aneieut  (djservations  is,  h(»\vevt;r,  j>iveii  witli  tlic  acceleration 

8".3- 
The  total  correction  to  tlio  mean  longitndo  of  Hansen's  'I'abU's  now  becomes 
-  i".i4-29".i7r-3".86r*-  F;,-o".09sin  J  -  i5".49rosJ: 

V-i  representinj;,  as  before,  the  empirical  term  (hie  to  the  action  of  W-niis;  A,  the  an<rIo 
l8  V —  i6  K  —  (f;  and  Z',  the  time  connted  in  centuries  from  1800. 

To  jrive  .1  (dear  view  of  tli(f  course  ofthe.se  corrections,  they  have  been  tabuhited 
tor  ten-year  intervals  from  i6?o  to  1900.  The  residts  are  shown  in  the  followin}^' 
table:— 


Year. 

A 

- 

■^. 

-l5"-5 
X  iosA 

Secular 
Terms. 

Total 
Corr. 

1610 

a 

306.5 

+ 

.5'.'3 

_ 

9.2 

+   39.0 

+ 

45.1 

30 

3I<).6 

+ 

.8.7 

- 

11.8 

+   37-4 

+ 

44.3 

40 

332.8 

20.8 

- 

13.8 

+  35-7 

+ 

42.7 

50 

346.0 

+ 

21.5 

- 

I5.'> 

+   339 

+ 

40.4 

60 

35<).3 

•(- 

20.7 

- 

15-5 

-t    32. 1 

+ 

37-3 

7" 

12.4 

+ 

18.5 

- 

15.1 

+   30.2 

1- 

33.6 

8.. 

25.6 

+ 

15.0 

- 

14.0 

+    28,2 

+ 

29.2 

i)U 

38.8 

+ 

10.4 

- 

12.1 

+  26.2 

■t- 

24.5 

t^<xt 

52.0 

+ 

5-2 

- 

9-5 

+   24.1 

+ 

19  8 

10 

65.1 

- 

0.4 

- 

f'.5 

+   21.9 

+ 

15.0 

ao 

78.3 

- 

5.9 

- 

3.1 

+    19-7 

+ 

10.7 

30 

91.5 

- 

II. I 

+ 

0.4 

+    17.4 

+ 

6.7 

40 

104.7 

- 

155 

+ 

3-9 

+    15." 

+ 

3.4 

so 

117. q 

- 

18.9 

+ 

7.3 

+   12.5 

+ 

0.9 

60 

131.0 

- 

20.  b 

+ 

10.2 

+   10.0 

- 

0.6 

10 

144  3 

- 

21.4 

+ 

13.6 

+     7-3 

~ 

1.5 

80 

157.5 

- 

20.6 

+ 

"4.3 

t-     4.<' 

- 

"•7 

<)0 

170.7 

- 

18.3 

+ 

153 

-t      1.8 

- 

1.2 

1800 

183,9 

- 

14.7 

+ 

IS-S 

—      I.T 

- 

0.3 

10 

197.0 

- 

10.2 

+ 

14.8 

-     4.> 

+ 

0.5 

20 

210. 2 

- 

4') 

i- 

134 

-     7i 

-(- 

1.4 

30 

ar3.4 

+ 

0.7 

+ 

11.3 

—   10,3 

+ 

1-7 

40 

236.6 

+ 

6.2 

+ 

8.5 

-    >3.5 

+ 

1.2 

50 

94Q.8 

+ 

II. 1 

+ 

5-4 

^    l(..7 

+ 

<).i 

60 

263,0 

+ 

•5-7 

+ 

1.9 

—  20.0 

- 

2.4 

70 

276.2 

+ 

19.0 

- 

1-7 

-  23.4 

- 

6.1 

80 

289.4 

+ 

20.  (J 

- 

5.2 

—  26.9 

- 

It. 3 

0" 

302 .  () 

+ 

21.5 

-- 

8.4 

-    30. 4 

- 

"7  3 

I()UO 

315.8 

+ 

20.6 

- 

11. 1 

-  34' 

24.6 

-^  - 

—  _ 





v-f. 


REsn-ARv-rrrEs  on  the  motion  of  the  moon. 


269 


It  will  he  iiistriictivf  f(i  notice^  liow  tlicsc  rcsiiltiiiji-  cnrrccfiniis  ((iiiiiiiirf  witli  tlioso 
wliich  liav('  Immmi  iilnfjuly  (lorliK-fd  tVoni  individiinl  oltscrvatioiis  ur  jituiips  of  uhscrva- 
tioiis.  This  is  sli.twii  ill  the  foll(.\viii}r  table.  'I'lic  ohscrvcMl  com't-tions  ami  tlic  pn.ha- 
ItliMMTnirt  -i-  f  arc  taken  without  chaiij^v  trmii  the  table  ffiveii  <ni  pajres  261  and  262. 


_  I   Observed   I  „         . 

°"'*-       Correction,    formula.    Difference. 


i6}i.4 
1630.4 
1633.3 
i;>35.7 
1639.4 


1645a 
I&45-6 
1652.3 
I6S4.6 

1661.2 
1662.0 
iMA.i 

1673.9 

1676.4 

16P0.0 
II 

1684.5 

16W.7 
1706.4 

1712.5 
•715.3 


172S.5     • 


78 
35 
53 
57 
34 
23 
»1 

34 
5" 
38 
31 

37 
38 
»5 

39 
83 

31 

21).  4 

34 

3« 

34.8 

24.1 


+  45 
44 
44 
43 
43 
43 
43 

41 
41 
40 

39 

37 

37 

35 

32 

31 

»9 

39.0 

37 

»7 

19.8 
16.6 


+  33 

-  9 
+  9 
+  14 

-  9 

-  20 

-  16 

-  7 
+  10 

-  2 

-  8 

o 

+  I 

-  10 

+  7 

-  8 
+  2 
+  0.4 

-  3 
+  5 


±' 

Wt. 

n 

'4 

25 

'3 

9 

II 

9 

5 

1  10 

8 

10 

8 

6 

5 

10 

4 
6 

5 

i.u 

4 

2.0 


14.8 

'39 

16.2 

■  2.6 

8.0 

12.6 

10.3 

12.6 

7.3 


7.5 


5.0 

7-5 
0.9 
3.6 

4.6 

2.3 

0,2 


0 

2 

0 

0 

6 

2 

5 

4 

0 

1 

5 

' 

5 

6 

3 

4 

too 

6 

35 

»5 

25 

45 
3 
I 

7 


Hy  conipann;,'-  tlie  corrections  with  the  probalih^  errors  it  will  be  .seen  tiiat 

The  rcmdiials  are  loss  than  the  probable  error  in  1  i  eases; 
The  re.sidtial".  are  eipial  to  the  probable  error  in  2  ea.ses; 
The  residuals  ,ire  ;;reater  than  the  ]iroliable  error  in   i.|  cases 

If  the  theory  were  itself  pert'e.t,  this  would  imlieate  that  the  |iiol)al)le  errors  assigned 
are,  in  the  in<-an,  .soinewhat  too  small  in  the  ca.He  of  the  eclipse  of  1639,  by  iIoki>'o\, 
it  may  be  re«rardcd  as  certain  tint  the  assigned  prolial)le  error  is  too  small,  as,  thron-li 
lnadvcrtein!e,  proper  accomit  was  not  taken  of  the  uncertainty  of  his  clock-correction. 


270 


RESEARCHES  ON  THE  MOTION  OF  THE  [HOON. 


Tlio  results  arc  divided  iiitd  jiroiips,  iiiid  the  luoaii  l»y  wciiilits  has  boon  taken. 
It  will  he  remarked  that  each  ;iroii|)  has  its  own  unit  ot  wei;>ht.  The  mean  results  for 
the  corrections  still  uutstandin;^'  will  then  ho  as  follows: — 

1635.9,  (5*— —  2".o  ±4"-2 

1649.5  —  i"-2  ±4"-2 

1662.3  -o".8±3".5 
1681.7  +i".3±o".8 

•6997  +5"-o±2"-o 

1706.4  +7".5_t2".o 
17 13. 1  +o".5±o".5 

1728.5  -o".2±i".5. 

It  will  he  seen  that  the  results  are,  on  the  whole,  as  ;;ftod  as  could  he  expected  except 
in  the  case  of  the  solar  eclipses  of  1699  and  1706,  where  the  <d»servations  of  L.\  Hiuk 
indicate  a  correction  of  sitscral  times  the  prnl)ahl(»  error.  Whether  this  arises  from 
sonn;  systematic  error  in  the  ohservations,  or  from  a  real  deviation  of  the  moon  at 
those  times,  must  be  loft  to  future  investigiition. 


§  16. 

OHSKUVKI)  LIMITS  Ol'  TIIH  MOON'S  SH.VDOVV  l)|T|llX(l  ITS  I'.VSSACH  OVKIl 
KNCLAM)  IX  TIIK  TOTAL  KCLll'SK  OK  171:;,  WITH  A  DKTKKMINATION  OFTIIK 
COUKKCriON  TO  Till';   MOTION  OK  Till;   MOON'S  NODK. 

The  most  I'emarkahle  and  valuahU'  of  the  oiiservations  of  this  e<'lijtse  were  those 
orj,nniized  hy  Hai.i.i'.y  for  the  purpose  of  determining  the  limits  of  the  shadow-path. 
As  the  duration  ot"  totality  incn-ases  very  rapidly  when  we  first  enter  the  limits  of  this 
path,  this  limit  can  lie  lixed  with  ^^reat  precision  i)y  an  i«l)servati<in  <>(  duration  inailo 
a  short  distance  within.  Sucli  an  observation  is  of  especial  value  for  deterininiujr  the 
position  of  the  moon's  node.  The  ujode  of  treatiujf  observations  of  this  class  is  as 
follows: — 

I'uttiuj;'  r,,  for  tlu;  central  duration  correspondini,''  to  the  position  of  the  ob.serv  ;r, 
r  fnr  the  ob.served  duration,  and  ^j,  for  the  radiu.s  of  the  shadow,  if  we  eompu  e  k 
from  the  formula 

the  .shortest  distance  of  tlit;  observer  fnnn  the  centre  of  the  shadow  will  be 

A  —  p,  cos  k. 
The  value  of  t^  is  given  by  the  formula 

r  - 11^ . 

If  iiirl\-  (lue  limit  is  ubserved,  this  result  will  be  subjtxtt  to  errors  of  the  semi- 
diameters  of  the  sun  and  uKton;  Imi  these  errors  will  be  eliminateil  from  the  menu 
observations  made  near  the  two  limits. 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


271 


IIr'  ahscrvatioiis  \vc  iii'c  ikinv  tu  use  nic  loiiiid  in   Ham.kv's   papor  in  tlic   I'hilu- 


softiiiriil  I ninsacfioiis  \i)y  1715.  I  ho  lixiiiy  <>l  the  exact  <((Mij>rapliifal  pusitndis  ot  the 
])lncc>H  of  (dmervatioii  at  lirst  picsfritcd  a  dinicuhv ,  wliicli  wascntirclv  iciiiovcd  tlimii^ili 
tlif  kindness  ul"  ( Jeneral  Sii'  Hknhv  .1  amks,  ( 'liiet'  nt'  llie  ( )rdnance  Snrvev  ut  Kn^iand. 
wild  sent  me  a  i-omplele  and  aecnrate  list  nt'  the  positicms  in  (piestiun. 

Tlio  I'oUowiiig  ib  u  rtuiiiniiiry  of  all  the  i)l(serv!iti<inK.  as  <^lv(;n  liy  llAi.iiKV: — 

A. — Sfafion!^  n> iir  Sditlhcrt:   Limit, 

1.  Norton  ('ourt,  ahont  10  miles  this  side  < 'anterhniv .  Oitserver,  IJev.  Dr.  .Fdiin 
IIakkis,  S.  'I".  1).,  It.  S.  S.,  IVel)endary  of  Rochester.  '  l>tn;ati«>n,  one  minute,  or  rather 
less. 

2.  Mocton.  ahout  midway  hetweeii  Norton  ('oui*t  and  ('anterlmr\-.  ( >liservers, 
the  inhahitants.  Kidipse,  liardlr  total,  a  small  star  lieinj;-  left  on  the  lower  part  of  the 
sun  at  {greatest  (dt>.enration. 

3.  (!ranl)rook,  in  Kent.  Observer,  Wii.i.iam  'i'KMri.r.,  Ks(|.,  U.  S.  .S.  Sun  extin- 
jfuislied  for  a  monuint  and  then  reappeared. 

4.  Wadhurst,  h(ivond  'i'nrid»rid;ie  Wells.     'I'otal,  Init  im  duration  jriven. 

5.  Ficwis.      Kclipse  total  lor  "sonu;  short  time". 

6.  Hri■^htlin;,^      Not  (piite  total. 

Tho  followinjj;  (juantities  may  he  assumed  as  liuvin^  tlio  same  value  for  ail  those 
stations: — 

\'alue  of  <^  or  di>tanre  from  place  of  reference 0.658 

Aujrmi'ntation  of  radius  of  sha-'ow 00305 

Hadins  (tf  shadow  on  plane  of  reference 012.S4 

K'adins  of  shadow  at  points  of  ohservation        015S9 

Helative  velocity,  or  >/  X-' +  K'" ('-"Ji'O     9.6720 

Duration  on  central  line 243".4. 

Wi-  now  take  the  stations  in  the  ordei-  in  \\Iiicli  they  are  ^iivcn. 

1.  X'litiiii   Ciiinl. — In    all   prohaiiility.    the    duration    was  iietweeii    52"  an-?   one 

minute.* 

If  r  =  52",  then  sin /,n  0.2  14;    A  =.01552. 
If  r  =()(/,  thi'U  sin /,  =0.247;    A  =.01 540. 

The  mean  of  thes<'  two  i-esnlts  is  .01546,  with  a  prohahle  error  of  les.s  than  6  in  the 
last  place. 

2.  Horloii. — 'The  sun  could  not  have  |ii-esented  this  iippearance  at  an\-  appr,  ,  lalile 
distance  outside  the  slcidow.  I'i'oliahly  the  point  was  exactly  on  the  limit,  the  sun's 
lind)  shinin<r  through  a  (U'|iression  in  the  moon's  liudj.  I'ossildy,  the  appearance 
descrihed  ma\'  lia\('  lieen  due  to  a  protnl»ei'ance:  Init  this  does  not  seem  likely.  Wo 
may  therefori'  put  Ar=.oi5S9. 

3.  CidiiliroiiL — Here  also  ohser.ed  A  =  ^j,  =  .oi5iSr). 

4  ami  5. — 'I'lie.se  stations  ;^ive  only  A  <  .oi5iSg,  hut,  in  the  case  of  Lewis,  proh- 
altlv  not  much  less,  since  a  duration  of  30"  would  correspond  to  A  =.01577. 
6.    liriiihtliiifi. — This  (udy  jiives  A  >■  .01589. 

*  Al  lilt'  timi'  ol  writiiiij  llils  I  iliil  mil  iiiilii;i.'  ili.ii  H  u.l.KY  eUttwIicre  k^vc  U.it.i  siidwiiiK  tin-  iliir.ilinii  lo  he ex.ictly  sip. 


272 


RESEARCHES  ON  THE  MOTION  OF  THE  MOON. 


Tln'  cotupiirison  of  tht'sc  n^siilts  with  tlio  tahK's  is  as  follows;  the  positions  aro 
those  t'liniisluMl  by  Sir  IIknkv  Jamks.  Tlu'  tiilHilar  values  of  A,  the  iniiiiiiiuni  distuiice 
of  the  point  of  ohserviitioii  from  the  axis  of  the  shadow,  are  coiiiputod  by  the  forinuljc 

of  v\  7  :— 


l.ali 

imic. 

Longiludc. 

Tabular  A. 

Oliservud  li. 

rorrccllon. 

Norton  ('oiin  . 

5' 

I  y .  f ) 

-  •4i).4 

+    .')I5'>7 

.01546 

—    .(HX)5I 

Hoclon  . 

5> 

17  : 

-   'j7-4 

.oif.7(, 

.1)1  fSt) 

—    .000l)0 

CranliiDok 

51 

5-7 

-  3a-4 

.Olf)83 

.01531) 

-  ■<'•")} 

Wailhutsi  . 

M 

3.8 

-  20.5 

.1)1624 

.01589  minus. 

—  .iKX)35  anil  more. 

Lewis    . 

50 

52.6 

-   0.8 

.i)i()5f) 

j  .()I58()  mit)us. 
(  .01577 

—  .txx)f)7  anil  nioio. 

—  .(XH)7i): 

HriKlolinR 

5" 

57-7 

—  aa.() 

.01740 

.01589  plus. 

-  .«m67  and  less. 

The  mean  of  the  first  three  results,  {fiviiiff  double  weiiflit  to  Xortoii  Court,  is 
.00071  J::.oooio.  Hut  sine*-  the  l.ewis  o1)servatioM  uives  a  iniiiiiiiuni  limit  of  .00067, 
the  most  prol)al)le  value  of  the  eorrectiou  may  i)e  estimated  at  —  .00075  -4-  .ooooS. 

IV — Stiidons  near  Noithnti  Limit. 

1.  Haverford-\\'(!st.  ()i)server.  Rev.  Uohkh  I'kossku.  Kclipse  total  a  minute 
and  a  half 

2.  Shrew.sbiiry  in  Shropshire.  (  Hiserver,  Dr.  IFoi.i.iNiis.  Duration  of  totality, 
I  ■"  40". 

3.  Darrin^ion,  al)ouf  2  miles  this  siih'  I'oiitefraet.  ( )bs<'rver,  TiiKoriiii.is  Si!i;i,- 
ToN,  Ks(|.  The  sun  rtJilueed  almost  to  a  [toint  resenildinj'-  the  planet  .Mars,  and  then 
the  li;iht  iie^iiin  to  ineri-ase. 

4.  liariisdale,  .'?  miles  south  of  DaiTinuton.      The  eclipse  "just  total". 

5.  IJadsworth.  Authority,  the  Hev.  and  Learned  .Mr.  I).\iiu /..  The  corona  .se(ni, 
and  iheret'ore  the  ecdipse  total. 

6.  Witley,  the  seat  of  I.,ord  Koi.KV.     Duration,  _5"'  15". 

\N'e  ha\e  from  the  (dements: — 

Hav.  w. 

.Mean  value  of  <? o.60(S 

.\u^inentation  <if  radius  of  shadow 002S1 

Radius  (tf  shadow  on  plane 012X4 

{{adiiis  of  shadow  at  station O'S^S 

Rcdative  v(docity (l..i>{>'.)  g.6S62 

Diiratiiin  on  central  liiu* ^^.'".o        2;6".6 

The  t(dlowin;;'  values  of  A  are  derived  from  the  obsei-vatinns ; — 

I.    Ihiri'ifind. — sin  /' —  .,5Sf^;    Azr.oi44^ 

2    Slirrirshiirif. — >iii  /r  —  .423;    A  =:  .01427. 

;.  IhiniiK/tdii. —  Here  the  phenomenon  corresponds  almost  (exactly  t(>  that  at 
Hiirtnn  in  the  south;    we  therefore  put  A  rrradins  of  sh.idow  —  .01  575. 

4.  Iliiiiisdiilr. — Same  vahu'  of  A. 

5.  liailmctnih. — A  <  0^575,  Init  prol>ably  very  little  less. 

h.  W'itliy.—Hit  far  from  the  limit  m  to  be  entirely  unreliable;  the  results,  howovor, 
nre,  sin  /.  =  .825;   A  =  .00891. 


OtlKTHt. 

0.6,^2 
.00291 
.oi  28.1 

■01575 
9.6805 


RKSKAKCIIKS  ON  TIIK  MoMoN  c)|     ||||;  .MooN. 


37.3 


Kxl.ilHtiii-  til,.   hilMilar  n-siilis  in  il,,.  .saiiic  lurm  ;i.s  tor  llir  m.iiiImtii  limits,  tlu-v 
will  lie  sli.iwii  ;is  Iwjluws: — 


Laritiutu.       I.iinniciulr.         T.ili.  i.  Olis   j,  Curr.  lo^. 


"■'^' 'I   W.  51  4S.1  f   .)  ;S.3  -    .,,u,s  _  .,,,4,3  ..  .^^,35 

Slii.wsl.uiy     .  52  12.5  f    2  41.5  -    ..,i2(.(.  -  .,,1427  I  -  .iKJlOi 

"•'"'"«'""       •  53  ^".5  ^     I  I'...,  -    .nun  -  .,,1575  -  ..^mXm 

"•""""'•'''••      •  53  3M  •     I  ii;  -     ..>.ui  -  .'..5-i  -  ..«.I34 

ll...lw..,il,  .      .  53  37. j;;  H,  ,s.„  -.01484  -  .oisfM:  -  ,„j„So; 

^^''''•'*  •      •      •  52  Ki.ij  1    3  20. a  -    .0.701  -  .U081JI:  -  .ooK^: 


Tllr    llli'MII    cnirrili I.livr,!     iV.illl    lll(.    tirM     turn-    st.ltiulis    is    — .OOOC/).        I'.llt     til,. 

•  •l«.s,TV:iiiuii  ,.f  tl.,.  .■,.i.,.ii,i  ill  |Sa,iu..rtli  w,.iil.l  iii,li.'al..  a  .■,.iT,.,-ti.n.  inmuTi.alK  less 
thai.  .n,),),yi.u|,i,li,  Ii.,u,.v,.i-.  Nv,.,.amio|  ivj^aid  as  cTtain,  .Mt,.-,tl„.|..  I  tliiiik  u."  may 
n  o-anl  — .oikkjo  as  ili,.  m,,st  pioltaMc  ciHTcctioii. 

W  ,.  tlm^  li;i\,.,  lur  til,.  ,.<.i.i.,.,.ti,m  1,.  the  tal.iilar  p-psiii,,,,  ,,\'  tli,.  -Iia.i..\v-|iatli: 

From  olt.sri'valioiis  ,.f  Miiitlitru  limit,  —  .i>,ic)75 
From  l^lls(.|\,.^ti,lll^  111'  nortlKrn  limit,  —  .ooocyo 
.Alcaii  coiTt.i'ti,!!!,  — .00082. 

Tlir  ..,.i|.,.,.ti..ii  ..xpn.ss,',!  in  1,.|iiis  of  th,.  yx-o,.,  iifri,-  <.o-,.nliiiat,..v  of  th,.  mo..ii. 
rt'lativo  to  tli,.  smi,  ami  of  the  iiio,.ii-s  |.anilla.\,  is,  in  m.it.s  ,,f  tli,.  5tli  [.lace  of  .l(.,.imals, 

—  o..|4  -HA  f  j;.;,  .H//  i    1.5  <UI. 

Tile  sail!,.  ,|iiaiitii\ ,  ii,.iiio.  (.xprcsscl  in  ti-rms  of  tlic  coiTcrtioii  to  tli..  hhmiu's  im.au 
loii^ilml,.,  ^  th,.  smi's  irm-  loiijiitiul,.,  L,  aii<!  iliv  .•onvi-tiuii  to  tliv  lon-iiml..  of  tli, 
moon's  noil, ,  is, 

''*-^  =  —  ^■2(i  ''><'  +  0.4  i^L  -f  2.4,)  >'iO  -j-  1  ;  ■>//  —  —  K>, 

ill.,  iiiiils  of  til,.  .•oi.n.,ti,.n>  l),.iiiii  s,.,.,.ii,l>  of  an-,  'riic  \alii,.  oi  -H^  -iv,.|i  l.\  ;ill  th,. 
ol.M.|.\atioiis  of  III,.  ,.,li|,si.  is  f  II  .2.  «hil»..  th..  fonmila  o.i\^.s  -f  1  >'.(>,  rii,.  iii.iM 
|tfol)al.li.  \alii,.  is  |K.||ia|)s  the  uiciin  ..f  tlu-s,  two  ivsiilK  ^.i  f  1  i".(,.  W,.  ii,.,.,..>aiil\ 
HiHijKWf  <^L  iiud  -W/  njiial  to  ziTo,  >o  that  ih..  Nairn-  ,>f  ')f>  iov  tlu>  i-jmu'Ii  will  Ik. 

,!!,'>--  iS"±5". 

From  the  ..,.,-iiliatioii>,  u..  Ii.iv,.  foKml  (|>.  235),  /  *^^  =  —  o".i4  ^  i".2,  wlii.li 
woiihl  ^ivt' 

I  li(.  moHi  ^Hojialili.  aii-aii  rtsuJt  l«»r  i;io  is 
for  1S6S 

*  I'll  I  1 1 1  rf  f^^<K  ^ilifi,:^  *r  /A  Cmmiiu.'V  u-  /*■   '/V.iwr./  ,./  / ;  -itu. 

:;.-, 7.".  Af. :: 


274 


RESEARCIIKS  ON    llli;   .MOTION  OF  Tlir  MOON. 


The  concrildii  In  1 1  \\si;\'.s  iiiuiiiiii  iil'  tli«'  iiionirs  iiuilr  ill  uiii-  ('ciitiirv,  llicrclorc, 
riiiMo  mil, 

+  i.V'.Ort4'- 

III  llii>  result,  hnwfvcr,  im  n('i;ilit  is  ;;i\cii  to  tlic  (tlisrrv;ilii>iis  used  liv  IIanskn 
liiiiisclt.  Allniifilicr,  I  tliiiik  wf  iiiiiy  rcnjird  llic  most  |ii'iili!ilili-  currcctiiMi  us  nlnnit 
1""-  TIk'  iiioliiiii  n|'  liic  iiiiilc  liciiiy-  iicfiiitivc,  this  fMiTtM'tioii  iliiiiiiiislii's  hotli  its 
illi>uli||c   \;i|ilr  mill   lllr  .lln  lllliilit  i>t'   l:ltilllil<-  li\    tllr  i|ll;illlitV 

in'  y, 

/'  liriiiii  cuiiili'il  ill  (tiiiiirii's  I'iniii  iS^ci,  This  icsiilt,  thoiiiili  iiciirlv  (•ciliiiii  with 
ifs|ircl  til  its  iilycliijiir  si^ii,  ciiiiinit  lie  rc;i;iri|ii|  lis  t|i'tiliiti\  r,  iis  it  will  In-  iitVcctcil  liv 
any  corn-ctiiiii  tu  Hansdn's  viiliic  (il'thc  niiinirs  pjiijilliix. 

foNCMiMNc    i;i:m.m;ks  on  thk  valik  or  tiik  skculai:  accklkuation 

IM.IH  (  i;i»    IN    THIS    I'AI'Ki;. 

Tlic  aiitlmf  Is  ciiiisciuiis  thill  llicii'  iiiav  lie  lunin  t'nr  iliirci'i'iiccs  ul' ii|(iiiii>ii  rcs|i('ct- 
iiu'-  till'  reality  ot' the  vcrx    laru'e  iliiiiiiiiitiiui  nl'  the  seeiilar  aeeeleratimi  which  is  imli- 

e.ileil   li\    the  |irerei|i|i^-  ilixMlssi.  Hi.       .\   e|(M|-    >||| .irv   ill'   the    eviilelli'e    iili    Imtli  sides 

<it'  the  ((iieslioii.  and  a  staleiiK'iif  <il'  the  data  li\  wliieh  it  mav  lie  settled,  iiia\  liiriii  a 
littiii;;'  riuielnslnii  \<>  this  iii\esti^ati<>ii.  in  the  tiist  jilaee,  ii  is  to  lie  remarked  that 
tiiele  are  three  |iieees  III'  e\  ideliee,  all  of  W  hiell  lllililale  a;,;aillst  till'  dimilllllloil  hen! 
di  cjihed,  and  in  raMirolthe  lar^ie  \,ihie  round  li\    IIaN'skn.      Thev   areas  follows: — 

I .  'I'llc  .s|||i|(osed  ,iii(iinl  lot.'il  eelijises  known  res|ieetivelv  as  the  «'cli|»M'  ol'  'I'ltAt.Ks 
and  the  ellipse  at  i.aiissn  If  the  total  eelipse  of—  5,S.|.  Ala\-  2S,  reallv  |i;isseil  over 
the  icLiioii  in  wliieh  the  ei  lelnated  hallle  descrilied  liv  IJKKoiions  is  sii|i|iosei|  to  liavo 

lieell   lolloht,   anil   if  the  eilijise  of  —  -^^f),    Mjiy    li,,  was  really   total  at    the  sll|i|iosed  site 

ot'  l.arissi,  then  no  apiireeialile  ehaiiii  '  "I  I1a.nsi:n's  loiijiitiide  of  the  moon  diiriiij,'  those 
times  is  admlssihle  The  reasons  I',.r  doiilitin^i-  the  realit\-  of  these  eeli|isesare  set  forth 
.^o  I'lilly  in  vN  ;,  that   lliey  lie 'd  not  he  repeated  here. 

-•  'I'lie  hin.ir  ellipse  of  — ,^Sj,  reportiil  as  ohscrved  at  Haii\loii.  It  is  certain 
tli.'it  if  this  eclipse  was  le.illy  seen  at  Hahyloii,  no  appreiialile  diniiniitioii  of  IIan.skn's 
longitude  at  this  time  can  he  admitted. 

;,.  Those  lunar  eidipses  cited  l)y  l'roLi;Mv  without  .i  stateineiil  oi'  the  phase 
.di>er\cd,  !;  lieiiiM  hithcit,!  ;issniiiei|  tliat  the  times  noted  are  those  of  the  middle  ol'  the 
eclipse.  Th'se  eclipsi  >  are  in  e\cry  way  so  iiiiceilain  thai  no  i^reat  stress  can  he  laid 
iMion  them. 


two  ; 


The    -oiirce.s  of  evidence   uliicji    indicate   the  diminiition  here  deduced  are  these 

(r.   The  I'loliniaic  eclipses  of  the  Afiiitir/r.s/,  discussed  in  >>  |  ol  this  pajier. 

fi.  'Hie  Araliian  eclip.ses,  discussed  in  v\  5. 

|{  |(|(i-«l  lie  n marked  that  this  is  not  a  case  in  which  the  discordant  data  can  he 
coml>im  d  hy  uiijihts.  The  e\  idence  iiu  liidi  d  niider  heads  1  and  j  is  either  coiiehisive, 
or  false,  and  thei'ej'ore  worthless,      liither  the  ,so!;ir  eclip.ses  were   total   at    the  points 


Ki.sr.ARciir.s  ON  Tin;  motion  or  Tin:  moon. 


'■7> 


sup|Misc(l,  or  tlit'N  were  iHit.  It'  llicy  were,  we  ciiiiiiitt  ••li:niiii-  IIanskn's  Idimiliulc  : 
it' tlicy  were  lint,  we  ciiii  (Iciliicf  ii(itlii:i;;'  from  tlicin.*  'The  same  rciiiark  ii|i|ill<s  t<> 
till!  liiimr  t'rli|is(!  of  —  _^Sj,  iiccitnliiij:-  to  \\li('tln'r  we  sii|i|mis('  it  to  iia\ c  liccii  n-allv 
st'cii  at  liiilivl.iii  or  Hot.  I  >atii  (r  ami  //  do  not  admit  of  l)riii<>'  disno.srd  ot  sd  pirrixlv, 
Imt  we  c.Miiiot  sii|i|io.sc  till-  accclcratioii  imicli  ^icatcr  than  S".:;  willioiit  sii|i|Misiiii;- 
systciiiatii-  <-rrors  wliicli  sci-iii  (jiiitf  im|iiiilialil«'.  '\\i  hk-  tlicsc  errors  srcm  more 
iinprolmhh' tliiiii  mistakes  ill  data  i  and  j,  and  tlieriturc  I  re^aril  the  'iiiall  \alne<d 
tlu!  scciiliir  iU'iH'leratioii  as  Iia\iiiji-  tlie  preiiomleiaiiee  nl'  evidence  in  its  faNor. 

'I'lie  Araliiaii  tdiservatioiis  are  far  more  reliahle  tliaii  those  of  l'roi,i:M\  :  it  i>  there- 
fore of  interest  to  know  what  sahie  of  the  secnhir  acceleration  woidd  lie  olitaiiied  li\ 
conil)iiiin;;'  iIh-iii  svith  the  modern  olisei'\ atioiis.  The  nncertaintx  n  >|ieciinii'  the 
inei|iialities  of  loii;^'  period  prevents  iis  t'roin  dedinin;^'  a  precise  n-snlt  in  this  v\ay,  Imt 
we  may  safeh'  sa\' that  it  will  ditfer  very  little  t'rom  7',  and  will  tliereloi-M  he  scarcely 
iai'^i-er  than  the  theoretical  \alne  of  the  accideratioii. 

Let  lis  now  view  the  (piestion  from  the  opposite  Ntaiidpoihl.  ( Jiaiitini:  tli"  naiity 
of  the  prolilemalical  total  eclipses,  and  theiet'oie  the  corri'ctiiess  of  IIanskn's  loiii;itiiile 
live  or  six  centuries  liefore  ('iiKlsr,  how  w  II  llii'  nndoiilited  eclipses  ot'  I'rtn.KMV  and 
the  Arahians  he  represented  .'  In  consider  n;;'  this  ipiestioii,  we  must  reiiieiiilier  that 
this  representation  will  not  he  the  same  as'hy  II\\si:n'>  iinalteivd  talih  s,  incan-i'  the 
modern  (dtservatiims  have  show  11  that  the  latter  need  a  correction  to  the  mean  motion 
of  the  moon  at  the  present  time,  and  the  M-ciilar  acceleration  must  he  taken  to  accord 
with  this  chanjic  It  will  he  rememhered  that  II.Wsi'.n's  \aliie  of  the  secular  ai-'elera- 
tioii  has  ill  itself  no  foundation  wliate\<'r  eitli>  r  in  oh.serxation  or  correct  theory,  ami 
iiia\'  therefore  l)e  chaii'jed  at  jileasiire  to  til  the  toiindatioii  which  wa~-  t'oiind  for  it  after 
its  deduction,  iiameh  ,  the  ancient  eclipses.  Since  it'  we  retain  it  iniaiiered,  and  admit 
the  mean  motion  of  the  moon  deduced  tVoin  niodiin  oli^eivatioiis,  the  ancient  eclipses 

will  110  loii^^er  he  repre-ellted.  We  lllllst,  ;.>  place  its  vallli-  oil  an\  I'ollllciat  ion  at  ;ill, 
cliailfre  it  so  that  tlle>e  eclipses  shall  he  represented.  'The  coirectioll  to  the  centennial 
ineiiii  iikotii'iii  jrivcn  li\  inodern  ol(>ervalioiis  we  luive  already  loiiiid  to  he  —  j<>  .2.  If, 
tlu'u,  we  ivjireseiif  hv  »Vs  flu-  correction  to  IIanskn's  .secular  acceleration,  tliu  total 
ctmi'ctioii  lo  the  moon'>  mean  i-iij^itiide  '/'centuries  alter  iSoo  \\\\\  lie 

To  re|irt-.ent  the  ancient  rotal  "■cli|»«M'>  as  n-ipiired,  tin-  jiiantitv  >lioiild  he  zero  alioiil 
five  anil  a  halt  ceiiliiri<s  }M*1i»i>-  <'ii«|]tr.  I'r  lor  T  zz  ~  -\v.V       This  condition  will  j^ive 

•J^r:—      .25  ;      =  10"  *> 

tor  ikv  secuiiu  aceeleia!         whit .    >»iU  .•  pn'>eiii  at  ihi    -ami'  time  the  m<wl«  111  <d»sei\,i 


*Iit  (•iiuuMimiilK  I'K'  »»»l<!«t.  I"  Miamifl  •*  »••  itttufwitnlr  ■|u;ililir.ilj()n  lii  luiiii  i'cini'lil>lv<-ni'<i'i  mi  ili<  'ii'-  lMrt>'.. 
UMil  falMit  aihl  u'iiilllli'»lM'«*  <Mi  llic  ml  rt.  Ilir  Jiiiliui  ri  hi^  mil  ^  >  iiiuiTi  In  llii  liisimii'  ii.iriaiivt'  j"  hi  iIi.iI  ■.iiiii\'u  1 1 
linn  III  llir  iiiiM.illvi'  III!  uliirli  llir  litpnll"  ''i''  '■!  .1  Inl.il  ii  lijis,'  K  Inuiiili'il.  .M.ikini;  allowaiii  r  fni  llii  i  K'aKi-i'i.iiiMh-.  ,iiii| 
iinrcrlaiiilii's  lo  wliiili  naiialuis  arc  liaMi'  wlu-ii  llirv  jiass  ilir<>iii;li  iiniiiliial  ntiinU.  In  rniisiiliis  il  iini  .ii  all  iiii|>i>>lial<lr 
llial  llir  naiialhr  nl  til  h'i':">M  '  ii'spi  liliiH  llir  li'iiiiiiiallnii  <jI  a  lialllr  l>\'  il.iiknrss  iiiav  have  oliuiiiali  il  Imiii  ,i  pailial 
n'li|isr  (i(  llii'  sun,  wliirli  ii'rtllinl  or  iii.|iirssfil  ilii'  roinlial  mis.  rs|ir(  iilly  jl  iliis  n  lijisr  ivas  aliiio-l  loi.il  wIiimi  iIic  smi 
srI.  Ilciic'o,  ronrriloin  llial  Ihr  |)lwnoiiiiiioii  iv.is  irallv  llu-  !•  lipvc  mI  -i''!,  lii-  I'misi.li  is  tli.il  ilif  ii.iii.iIk  i- iloi  s  iioi 
enable  us  lu  decide  wluilici  llic  f  lipsu  wjs  tulal  ui  |iailial. 


276 


ri:si:arch!.s  on  riir.  moiion  oi   iiii.  mkon. 


tiiiiis  iiiiil  till'  li'Iiil  (Mli|(M's  III'  'riiAi.iis  iiiiil  l-iiri>sii.  'riic  (•(irrtM'tioii  In  llic  iiiuMirs  iiicaii 
lMii;^itii(lc  7'ciutiirics  mI'Iit  iScio  will  llicn  l)r 

-  7' (29'+  \".2S  '/•). 

Wf  now  di'siri'  to  kimw  limv  tlii'sc  cnrivi'tiaii-i  will  .iltcr  tlic  rcprcsiMitiilinii  of  tlic 
rtoli'iiiiiic  iiml  .\r:ilii:iii   CI  lipscs.      I''i»r  tlir  tciniii'r.  llic   ii'|iri'>('iiliMinii  will  lie  siiloliiii 

ti.ilK   till'  s ;!■>  1)\    tlir  uii:illrri'(l  till  ill  •>  III'  II  \\si;\,  litiimsc  tlic  I'iictui-  2()"  -|-  I  ".J  5  T 

V.'lllislics  ill  llif  rciiiisc  III'  till'  iilisiTMltiiills.  ir  till'  illirifllt  siiljir  i'cli|iscs  illT  ri'ill.  wr 
iiiiist  still  >ii|i|iii>f  tli.il  till'  •j:vf.{{  iii;is>  III'  I'loi.r.MN's  iclipsi's  :iii'  iinii'c  tliiiii  liiill'  .111 
Imiir  ill  I'lTiir. 

I'"iil'  till'   Alilliiilll   rrlijisrs,    7'   IMllp-s  rroill  —  <).7  tii  -So,   illlil   tl|r   r' i|isim|||i'1iI   rnr- 
|•|•^li(lll^  In   tllr   l:llilll:ir  llirMll   1(  illilit  l|i  li  -  ill' till-  llliinll  fll'i' : 

For     S29,  (U  r:  -|-  2'.- 

VilV    lOlXI,    'W  n  -f-  2'.-{. 

'I'll  Iiml  Imw  llir  Ar.ilii.iii  nli^iTviitiniis  i(|iirsciit  tlic  rcviscil  tlicnrv.  wc  iimst  sii|i|iiisc 
tliiit  ill  tlic  iiiiii|i;iri>iiiis  ;^i\cii  mi  piiuc  5  ?  tlic  tnliiilnr  litii;;itiiilc  is  iiirrciiscil  Iiy  these 
iiiiiiiinits  licl'iirc  liciii;,;'  i'iiiii]i,iriil  willi  niiscrv  .itinii.  Wc  iiuist  tlicri'l'ttrc  iijiply  flicsc 
\illllc-<  III  'W  llcniltiv'i'K'  til  tlic  ciilllliili  Jl  til  iilit;iill  the  new  eiilTertiiills.  'These  new 
(■iiriciiiiiiis  ;ire  then  cuiiMTteil  iiitii  time  liy  ili\  iiliiiL;-  them  liy  the  ruetnr  /',  whei'cliy 
we  iilitiiiii  the  riilliiwiii;;'  enn'cetiiiiis  In  the  IiiImiIjii-  times  nixcn  hy  fill  the  Aniliiiin 
iiltscrxiitiuiis.  Ill  iinlci'  In  fncilitiite  11  iliscnssinii  nl'  the  results,  and  the  ileteetitni  hI' 
imv  s\stem!itie  ermr  iimnii^'  the  niiscrv  jitimis,  ;i  tlireernlil  cl;issilii;itiiiii  is  iiunle  m  eiinl- 
illi:-  In  whelhcr  the  eclipse  Wils  nl'  the  sun  nr  nf  the  liinnli,  whether  the  he;,;innillji-  '"■ 
ciiil  w:is  nli>er\ci|,  mill  whethei'  the  iiltitinlc  mi  which  tli"  time  ilepeiuls  niis  iiliser\ci| 
ciist  iirwcst  III'  the  nil  riili.in.  'The  hitter  ilistiiictimi  is  impiirtinit,  heciiiise  nny  emi- 
sfnnt  crrni-  in  ileterniiiiin^'  the  ;iltitiiiles  will  Iiiinc  iippnsile  ell'ecls  on  the  two  siih'.s  of 
tile  mci'iili.'iii. 

IIAGHAII. 


Vciir  .S-0.   K<'l.  0.  iie.i:-.,   'W-((  5i"'i   Alt.  Iv 


S:i) 

0 

Km! 

+  -M 

■^54 

1) 

Mcjr. 

+   >2 

S5f, 

D 

itc--. 

h    9 

923 

1) 

Kiiil 

I  12 

02;, 

0 

Knil 

1  ^:. 

925 

3^ 

He}.-. 

1    1 

925 

D 

Knil 

-\'  7 

927 

1) 

r*  • 

—  s 

.,2.S 

0 

Kuil 

-1-  16 

9-9 

1) 

1  ten* 

(-33) 

9:;  3 

3) 

Hojf. 

+    7 

i<: 

RESEARCIIKS  ON   Iiii;  motion  oi-   mi.  moon, 
CMI.'ii. 

Vi'jir  977,    KrI,  0,  |;,.o,,  (.V),  ,j/-   j.  If,'"     .\|,    |.; 


•/  / 


'HI 

0 

Kii.l 

-f-  (.. 

1;. 

97.S 

0 

15.-    (.S) 

f  31 

W. 

97s 

0 

I'in.l 

+    9 

w. 

079 

),j 

Kii.l 

+  16 

1 

07') 

© 

|{'-.    .S) 

+  15 

w. 

9;t> 

2) 

!!'■;:. 

-f    8 

H 

979 

]) 

KimI 

-f-  1') 

\V. 

9.S(0 

2) 

Km.I 

+  10 

; 

9S. 

3) 

I'..-. 

■\-     8 

w. 

98  r 

2) 

Km.I 

+    3 

» 

981 

]) 

I5..0.. 

■\-  20 

w. 

9«3 

2) 

Kii.l 

+  - 

\\. 

9«5 

0 

li.- 

+  3<^ 

\\. 

9S5 

0 

Km.I 

■1-  10 

w. 

986 

2) 

It.-    (.V) 

-f-27 

\\. 

990 

2) 

l'..r. 

—  20 

v.. 

993 

0 

II.-. 

-1-     6 

K. 

993 

0 

Ki^.l 

4-25 

K. 

li)02 

2) 

li..n. 

+     6 

v..  .'ihil    f 

-10'"  w. 

luu} 

0 

!!<•;:•. 

f  ir. 

\v. 

T.ikiMt;   llic  Mlc;lM>  liy   .liLssi's,  \\r  linil  ; — 

I'VtIMI   0,     111  — illlliMli',     Ml.'.lil     Si—     I      |(/" 

0,   Kii.i,  -).,  is 

J),    n(';iiiiMiny,  4-    6  ..r   (-9'" 

2),    Kii<l,  -f    9 

'I'll.'  Inrov  ,lili;.iviHv  l.chv.TM  tl...  sul.ir  iim.I   liniiir  ,..li|.,s..,  .■,ris..s  Im  |.;ii-|  IVhm,  iI,.. 

lu.'t   timl   i.   .•iliUI-..  il,   tl,..   , m"s  luMni,,,,!..  will   -..)..T.lil\    ,;it|s..  ;,    UT-Mfcr  .•|,iM|..v  i,,  ,1,.. 

»'""•  '••'  •'  '""■■"I-  lln.u  i;,  that  ..r  ■•,  ,>nlnr  ...■lip.s...  Tli..  tun  nu^nis  H„-  }*  l..-inMiiM.  ;mv 
•  l.'rivc.l,  till.  „ii(!  !.>•  ivIniiiiM-  mii.I  tli.^  ..iIht  l.y  ivj.M-liM-  tli..  .Iis,-,,n!.iMl  ..l..s..rvri(inM 
of  990. 

Im    III.'    I!:.h',I.mI    ...•Iii.s..s.  ill,.   al|ilM.l...s    uviv   all    nhs.TV  ,,1    \n    lli,.  rasf,  su  ||,al   u.. 

sli.ml.l  ..iMit  ih.Mii  .'iitiivly  ill pariML;  rasl  aii.l  wsl   ..l..s..r\ali..Ms.      Ki-hm  tl...  Cai,,, 

«'fli|iscs,  we  Iin\.' : — 

•^l'';iii  ivsmIi  Ir a^l  ahiiiiil.s,  A/ —   |    7'"  ..r    |    12"', 

M.'cc.nliMi;-  asllic  .lisoiiilaiil  ..liscrvatinii  uJ'q.m.  is  ivtaliic.l  nr  ivjr..l..<|  ; 

.Mean  ri'.Milt  Ir wc^t  altitM.lcs,  A/~  j-20'". 

That  111.'   |H.,sltiv.'  .-..nvftion   ..f  ten   ,,r  |ilt,.,. iiiiit...^  thus  iii.li.at.'.l  >Ii,.mI  I  1... 

'""''•''  '^ '"  '"  ""•   '""  '•'■  »'"'  M"'-''I'"i       II'  ■   Ii.hI    to   ..s|,lalM    Ihrir   vality.  tl,.. 

ni..sHialiiral  way  ..f  .loin- so  unul.l  h..  t,.  mi|i|m.>..  thai  th.' .,l,s,.|\aliuMs  vn-,-,.  (a.n'iMav.l 


27% 


UESRAuriiLs  ON  nil:  moikin  or  nir.  modn, 


with  to  -nil  Millie  lliiiiiy.  r>iil  llii>  cNipl.-iiiiitiuii  sicni-  iiiiiiliiiis>ililr,  lic(;iii>r  llir  tnii- 
sisti'iir\   with  llic  iiHMlirii  iIkih'v   nf  tlic  iiii'i|iiiiliti('s  ol'  till'   siiii   .'iiiil    iiiiMiii  is,  I  tliiiik, 

;irfllt«'r  tllilll  lllllt  ol'tllr  lust  llicmy  tlir  AllllliilllS  nilllil  li;i\r  cnlislrilrtcil.  'I'llis  cnll- 
sidiTjltinli  seems  tu  me  III  lie  (•(i||rlllsi\  e  in  tiUtir  ii|'  the  ;;elillillelie^>  ul'  the  Alilliiilll 
nils!  rv.itlulis.  'I'm  sil|i|iuse  llie  (lil]'el'eliees  |ii  result  iVolll  |ilirel\  ;i(eii|eiit;il  eiriils  seeing 
>ii  |;ir  Ii(\iiimI  llie  iiiHIllcU  ( li  re.'Isi  iM;lI  lie  Jil'i  ili.l  liilit  \  tlliit  im  ilisrll»iiili  id'slleli  :i  |ini|i- 
•  i^ilioll  is  lleces>iil\  .  .\|i|i:irelitl\  ,  I  liilel'i  nc.  we  r.ili  li.r-ill\  ;i\iiiil  ;ie(e|itill^  ime  ul' 
tlle-e   |ir<i|iH>itiii||>  ;  — 

l.itlier  tlie  recently  ilece|ite(|  Miillenl  llie  ,l(  celer.lt  Ic  ill  .'ilul  tile  llsiliil  inlel'|ireliltii  ill 
(i|  llie  illieielit  si i|;ir  eclipses  ;ire  In  lie  r;ii|ic;ill\  .lllereii,  tlie  edili'ie  ul  -  ^  V  Iml  li:i\  ili^' 
lieeii  tnliil  !it  Liiiissii,  .iiiii  lliiil  nj  —  5,S|  nut  Iiiixiii;^-  lieeii  tiital  in  .\>i;i  .Minur; 

(  )|-  tlie  me.'in  niiiliiMI  ul  llie  muiili  is,  in  the  nmrse  ut'  celitnries,  slllijecteil  til 
dummies  >u  wide  llial  it  is  nut  |ius-,il(le  tu  iissii^n  a  ilelinite  \iiliie  lu  tlie  secniiir  Jicct  I- 
enitiun. 

In  cuiiclnsiun,  it  m:iy  lie  interestini;-  lu  iiKjiiin'  what  liy:lit  uflur  material  tlian  lliat 
ilisciiNseil  in  tlie  |ireceilin^  |ia;i('s  may  throw  on  the  ijuestioiis  at  issni'.  The  must 
iinpurtant  >i|  these  i|iies|iuns  is  that  ul'  the  niuon's  mean  lun;:'itnile  tVum  twcnix  lu 
lweiit\  t'uiir  ceiiliiries  ai^ii,  nil  whicli  iimsl  iie|ieiii|  uiir  iiiter|ire|,itiuii  ul'  the  ancient 
sular   ecli|ises.      I    Mill    awai'e    ul'   unl\    t  w  u   classes  ul'   (lata    which   can    lie    reasunalih 

e\|iecteil   tu  thi'uw   li^'lil    ii|iun   this  i|iie>tiuii   separate  IVum   an\   tlieuiv   ul'  the   n n's 

uiutiuii  ruiindeil  uii  iiiiiileiii  uliserv  atiuii>.  The  first  ul'  these  are  histurical  tutal 
(•(•lip>es  ile^criliiil  ill  uther  writiiiL;s  than  iIium'  ut'  the  (Jreek  ainl  liuiiiaii  classic 
anthurs.  Sume  ul'  the  ( 'him  >e  eclipses  were  iliscnsseil  li\  Srii.ii;i.i,i;i;i  c  in  a  paper 
preseiileil  |u  the  Maiiisii  Aca(leiii\  ul'  Sciences  aliunt  1S75.  'The  remains  ul'  Ass\riaii 
talilet>.  ili-cu\ereil  ilnriiiL;  the  last  lew  \ears.  conlain  ilescriptiuns  ul'  ur  allnsions  to 
eclipses  which  iiia\  hereailer  lie  rc.iiiiil  tu  he  luial.  The  uther  class  indniles  tlieucciil- 
tatiuiis  of  stars,  or  the  positions  of  the  mu<in  relative  to  certain  stars,  which  are 
tlescrilieil  liy  I'luLi'.MV  in  I'luulv  \||  ul'  the  ,!////(/'// s7.  Ill  this  class,  we  mi;iht  alsu 
inchiile  the  siicalleil  eclijise  ul  TiiKuN,  desciilieil  li\  Tiii.iix  in  his  cunmieiitary  un  llie 
Alniii<ii  si. 

The  antliur  has  nsed  iiuiie  ul'  this  materi,;!.  Iiecanse  the  whule  ul'  it  seenieil  tu 
he  iinreliahle.  It  has  heeii  his  aim.  in  the  preceding:-  invcsii^atiun,  lu  cuiiline 
liis  (lisciissiuii>  to  iiliserv  aliuii--  which  cmild  he  received  with  suine  appruach  tu 
entire  cunlideiice.  I  lad  uther  material  lieeii  admilted,  the  |trulial)le  result  wuiilil  liav c 
lieon  a  ;:reat  mass  uf  discurdaiit  resiills,  miicli  ul'  win  di  vvmild  have  tu  lie  rejected  on 
accuunt  ul'  its  iiicumjialihilily  vvilii  utlnr  puiliun-.  The  result  to  he  linallv  accepted 
would  then  have  depended  very  larticlv  on  what  uliservaliuns  were  rejected  ami  what 
relaimd,  and  this  wuiild  necessarily  have  depended  uii  the  indiiineiil  uf  the  investi- 
jrator.  it  would  hardly  have  h  en  jiossilile  to  have  lorined  ^mdi  a  jiidi;iiieiit  without 
the  suspicion  of  its  lieiiii;-  inlllleliced  liy  his  i\  ishes  or  prejudices.  It  thereloie  seemeil 
Itelter  to  avoid  this  necessity,  as  I'ar  as  jiossilile.  hy  einployin;^-  no  maleiial  mi  the  jicn- 
eral  relialiilitv  ol'  which  tlie  author  vvuidd  have  I'elt  niiwilliii;;-  to  stake  the  euirectness 
ul'  his  cum  lusiuii,  ur,  speakini;  mure  |ilainly,  which  lie  wuiild  have  meant  to  retain  if 
il  came  out    ii;;ht,  and    reject  if  it   came  out  wruii;;-.      It  was,  of  cuiirse,  im|iussiliU'  tu 


Ul.si;.\K(     11  ^  (IN    1  I II  Mill  ION   (II     II II.   Mm  i\. 


r7«) 


liiiN'c  MM  ;i>>iii'aii('('  III  cscrv  iliiliiiii  |ii'ii\iiiL:  ('iiin|i;itilil<'  >\itli  iNcrs  iitlicr  niic,  iis  is 
^liiii\ii  li\  ilii'  r('i«-('iiiiii  11111111'  I'tii!.  iiuiic  Mini  two  nr  ilii'ic  AiMliiMii  i'i'li|iM'>.  Itiii  tliis 
|ii'<i|ii>fiiiiii  III  rcji'i'li-il  iiiMici'iiil  scciii>  siiiiill,  niiisidcriiii;  till'  iicci '^.■>Ml°\  iiiiicrlMiiiiv  uf 
till'  I'liMimi'ls  tliri»ii;^li  wliii  li  tlic  (ilisi  rvMriiiiis  Iimvc  i'(  iiclicil  ii>. 

Niiw.  ri-liiniiii;:  l<i  llic  niMtciijI  wliicli,  iIkhi'^Ii  rcji'dt'il,  iiim\    imi  lie  \mIui'Ii'>s,  ilir 

(illjcclioll  III  lllr  ll-<c  III'  llli  (  'iiillCM-  Mini  .\>s\riMll  i'(!i|i-.i'^  wm-  ■.lllislMllliMlK  lllr  ^Mlllr 
MS  tllill    III   llic  clif^sicMl   l'cli||si   ^:     llir   Ml  rnlllil''   ills|iil'i'i|   Ho   I'I'MMIIIM  lllc   I'Cl'iMilll  \    IIimI    IIii- 

(■(•li|iscs  were  scvcimIIv  I.iImI  Ml  (I(  riiilli-  |Miinls  ul'  ilic  cMrtli's  siii'Imcc.  'I'Iic  (icriillMtiinis 
ciIimI  1i\-  I'iKl.r.MV  seemed  Wnl'lllS  ut'  lilnl'e  ciiuliileiK-e,  Mini  I  Weill  ^.  i  JMI'  MS  In  iiimIm'  il 
>iiiniiiMrv  III  l'iiii,i;\n's  slMliineiil^,  Inn  tliey  were  -i.  Imi-  I'li'iii  liein;^  preci-e  iIimI    -iiiie 

liesilMl.i  \-  WMS  jell  ill  ileiidili;.  wllethef  tlleV  Here  Uollll  elll|ilii\  illji'.  I  lillMlK'  (•nil- 
cImiIi'iI  !  ■  iiMlil  tlleili  iViilii  llie  ImcI  iIimI  lliev  H'e  ciled  li\  |'|ii|.|:>n.  lint  fur  tile  |ini'|Mi>e 
III'  |ireselllill;^'  M  (•ii||i|ilele  series  (if  i  •liserVMliii||>':,  lillt  |i>  |i|ii\e  li  il  llie  elTnliei  Ml>  vmIiu- 
111  llie  ciill^lMlll  111'  |irece-^iiill  ilediiced  lt\  Illll'Vlii  III  s,  liMllli  l\,  iille  decree  ill  M  eell- 
llll\  ,  vvii.H  Cdrfect.  II. 'ill;;  ill  mII  |ir(il'.tl(ilil  \  selected  I'nf  fin  |iii|-|mi-  nl  |iiii\ii|H  i\\\ 
elTiilieiills  li\  |iiitlie^is,  it  wm-^IimIiIK  |i  -silile  In  eilljiliiV  lllelll  willlnlll  llie  Ii'mIV  MtiiHI 
mIiiiM-  Mllildi'd  In.  tllMl  tins'  >lliilllil  II'  Mecepted  nl'  n  iecled  Meenrdiii;;  Ms  llieil'  renlllts 
I'lid   nr  did    lint    M^^Tee    Willi    llliise  i|eri\ed    llnm   iillier  iImIM. 

The  ecli|i>e  (if  'rilKiiV  WMs  nliserscd  in  the  Vcmt  ;'i|.  Ie>s  tliMIl  live  eellfllfies 
Iw-fiire  the  ciimillelieenielll  nf  the  series  <,f  ('('li|iMS  i;i\  eii  li\  IHill  .I<il  M>.  Il  m'cIIIs  In 
IIU-  sciircely  WnrlllX  III  rnliliilellie.  lie  lieMin,  |i\  •^iMlillii-  IIimI  he  MCeltlMteh  eMlelllMled 
the  lime  I  if  lH';>'illllil|i.',  Mini  fmilnl  it  in  lie  tWii  limii  >  mi  id  lil'l  \  lllillllte^,  Mild  then.  tllMl  liMN  - 
in;^  fiirctiiily  nliscrveil  ilie  time  nf  l»ejjiiiiiiii;;r,  Ik  niiiid  it  exMclly  the  smiiic.  The  lime 
nf  elidiliy  is  ;;isell  ii-  •'►"^TVcd.  Mild  M>  il  WMS  lini  stMted  In  llMVC  lieell  liredieted,  less 
>ii»jiieini>i  may  MllMeh  i<  it  In  Im  Mlisenee  III  ;ui\  iiidieMlinii  hnw  hi-  limes  were 
deTtTlliilied,  Mild  ill  llie  l'>|ii('inil-  e.  liliiidillee  nl  '  'iser\eil  Mild  enlll|illted  time  nl 
lie;:iimiii;r.  Ii'  ^m  \  imlliiiii;  nl  m  n  rlMiii  ii^^iniiess  which  runs  thi'niitih  lii>  iiMrrMliNC,  il 
seems  III  me  tllMt    We   llMXC  rcMsnli   In  |iImi  '■  this  ec|i|iS('  ill   the  SMIlle  CMl('^ii|'\-   with  nlher 

rejected  iMMteriMl. 

I  Irillllill^i'  lIlMt  the  .|llestinll  W  Inlhi-r  II  \N-I a  LiIiIiImi  iiIi'MII  Inlli^ilnde  nl  llie  mnnll 
dne,'%  nr  dues  lint  rei|ll!l'  M  lMr;ii  i|i';4'Mti\('  Ci>rre(  !iiill  diirill;:  the  celllmies  which  i;re- 
cedeil  the  ('hiishMii  eiM  ^  which  (|Me«li(>ii  I>*  tin  rninlMmeiil.it  'Mie)  reiiiMiiis  undecided, 
the  i|UeNiinn    iiiMXMri-i-   liiiw   Mdeii-i\('  ;ni-\\er  cMii  lie    ri-.tcln  d.      'I'his  (|e|M'iids   iijinii 

whelhel';:  cnl'I'ecl  llienl'N'  <i|'  the  M|ipMreUl  illei|UMlil!es  ni  Inll^  pelinil  in  tile  llinnli's 
mcMIl  mnlinll  CMII  lie  cnlistnicti  d.  If  such  M  tlienry  cMUIlnt  lie  I'nrmed.  Mint  if  the  mi'MU 
lUdtioil  'i!  I'l  mnnll  is  suliject  In  such  chMU;^i's  frnlii  /e  In  M;ie  tliMt  lln  cnli-lMlit  Mild 
wcll-ilelined  mIuc  cmii  lie  MssiMind  In  llie  sccuImi-  MccelerMlinii.  then  if  is  i,  certMill 
tilMl  the  |ia  ii'iM  ('Mil  e\  cr  lie  i  nnilil-i\  cIv  settled.  Iu'CMUm',  ill  iIun  cm-i  .  Mil  en.  lllsiilll 
CMII  lie  ilfMN.  II  frnlll  nlisi'l'V  Mt  inllS  lIlMile  Mt  Mil  \  nlhef  lilUC  lIlMll  dlirill^-  e.r  I'cMI'  tin  |ii  lin(l 
ill  (|lle>liiin.  'I'lle  nlih  colirse  W  ill  lie  In  IMMke  M  ciilU|ilete  re-l'XMlllin.ll  inii  nl  mII  M'  flit 
ellipses  Mild  nlher  (hltM   wllicll  lllMy   llirnw    liLlhl   nil    the  i|Uestiiill,  Mild    In  c  II  ipMl'e  ll'»-lll 

with  the  I'oiill-  iA'  ihe  Iwn  ,  v  pntheses :   lir-t,  tliMt  I!an>k\'s  T.-diles  Mfe  (in    d  diiriutf 

the  perinil   ill   i|lle-linn:    Mild,   M'Cnlld,   tllMt    llle\'   reiplil'e  il   cnrrectinll  nl    si\t(  rl'    IllillUteS, 

suljIrMclivi'.      Shniild  llie  i'\ideiice  pnt\u  to  \}c  iiiMiidy  in  luMir  of  nne  hypoti  e.s'*,  that 


38o 


RESKAUrilKS  ON    llli:  Mdllii.N  oK   llli:  MDiiN. 


Il\  |iiithr^i>  WiiIlM   li;iM'  to  Iti'  ;iri'('|ili'il  ;    ■<lli>i||it  i|   Im-  lli>|)i'lt'.s^>l  \  .  ilisfitrilailt,  I  lie  i|Ur»l  lull 
Wniilil  iTiiiiiili  llliilcciili'il.      'I'liu   illltllor  winilil  lie  vorv  >x\n>\    tn  st-c  the  (|llcNliiiii  cmimi 
iiiril  ill  tliis  wiiv  liy  Hiiiiir  iiiilf|ii'iiilfiil  iiiitlmriiy. 

ir.  nil  till-  utiicr  Ii.'iimI,  :i  |ii  rlrt't  tlii'iirv  of  iill  tlic  iiii'i|ii.ililii's  in  tlic  iiiiM>irH  iiit'.iii 
iiiniinii  I'.'iii  III'  I'lii'iiK'il  iiiil('|ii'iii|i'iitly  of  iiliscrviiliiiiis,  till-  i|iirsiiiiii  will,  in  nil  |ii'iiliiiliil 
il\ ,  Miliiiil  III'  lirinti  sitllnl  liy  llir  iiitiilcni  nlisiTvatiiMiH  ainiii'.  ( )ii  |i;i;r<'  25  of  tlic  [trcH- 
fiil  |i;i|ifr  is  ;;ivcii  an  fstiiiiatu  sliiiwiii;;  Imw  acmralely,  on  llic  liy|Mi|lifiis  in  (|ii('>liitii, 
till-  Hci'iilar  acceleration  can  lie  ileterinineil  wlieii  the  o1iser\ation.<<  lielweeii  iCiH)  anil 
I  7^0  are  siilistilnteil  I'lir  llie  ancient   olHervatioiis,     ( 'oiii|iarin;i-  the   proltalilti  errors 

there   a>silllleil  with   lllii-e  111'  the  lilial   re>llll<  ;^i\('ll   in   the  [ireceilin;;  sections,  it   will  lie 

Keen  that  while  the  results  ol'ilie  iitiseiN  aliiMis  near  1700  are  perliaps  a  little  less  accu- 
rate than  is  there  assnined,  those  lietweeii  l();,o  anil  1670  appear  more  accurate. 
Makin;;  the  most  lilieial  allowance  I'ur  iiiu'ertainty  of  every  kiml,  the  prolialile  error 
111'  the  Mcniar  acceleration  u>  lie  ileri\eil  Iriin  the  iiniileni  iili>er\atiiiiis  aloiie  cuiilil 
searceK'  ainolinl    to    1"   in    the    case    silppnseil.  ami   \\ollhl   lie    colisiileialily   leillHeil   liy 

the  iiliservations  which  will  lie  iiiaile  lielore  the  emi  of  tin-  present  century.  Since  tlu- 
conipetinu'  \aliies,  S"..|  ami  !<)".(),  dilVer  I'roin   each  other  liy  ^".5,  11  result  ilerived  in 


llle^^a^    wi'  ha\ c  ile^crilieil  wuiijil    In     llkel\    to  ileriil 


liel 


ween    them    it     It.' 


I  I'll 


l.alih 


erro 


r  was  1",  ami  woiiM  he  almost    sure   tu  ilu   sn   il    it  iliil    not    exeeeil  i)".5,  which  I 


think   Wiilllil   prove  to  lie  the  c; 


( i,  ' 


'-qV-     / 


.,/•''< 


7'^1 


